Calculating Savings Amounts Required to Reach Financial Goals

1. Life as a Series of Cash Flows

Many personal financial decisions involve money received now or in the future and often a series of cash flows known as annuities, which we learned about in the prior lessons. If you were thinking that loans and investments are like annuities and involve either making or receiving payments with interest over time, you are correct! A loan involves regular payments that include an interest expense and the original loan amount, or principal.

To address some of the most common financial decisions, we need to ask a few questions to determine what we are trying to solve. If the answer is yes, then the correct formula is noted after the question:

Question 1: A single cash flow to be received or paid in the future?
Formula to use: Future value (FV)

Question 2: A single cash flow to be received or paid today?
Formula to use: Present value (PV)

Question 3: The value in the future of multiple equal cash flows received or paid at regular intervals?
Formula to use: Future value of an annuity (FVAN)

Question 4: The value today of multiple equal cash flows received or paid at regular intervals?
Formula to use: Present value of an annuity (PVAN)

Note: The PV or FV of multiple unequal cash flows received or paid at regular or irregular intervals must be calculated separately using the formulas in Questions 1 or 2 above.

terms to know

Principal

The original loan amount.

Multiple Unequal Cash Flows

A series of cash flows of different amounts received or paid over time.

1a. Mortgage Calculations

If you are an adult who wishes to purchase a home, you will have questions about home loans, such as mortgages. For example, let’s say you find a home, and to make the purchase, you must take out a $150,000 mortgage, paying it back monthly. After checking mortgage interest rates online, you find the best option is a 30-year mortgage with a loan rate of 6%. You might be wondering what your monthly payment will be.

What you are solving for in this situation is the unknown monthly payment (PMT) that will be paid to the bank every month for 30 years, or 360 months (t). Since you will make regular cash flow payments on a loan of $150,000 (PV) that you receive today to purchase the home, you should use the PVAN formula.

Note: Since the payments are made monthly, the interest rate of 6% needs to be converted to monthly, and the number of periods needs to be in months when the PFIVA is calculated. Therefore, the monthly rate is 6%/12, or 1% (r), and the number of months is 12×30, or 360 months (t).

Now, we can substitute the loan amount of $150,000 as the present value of an annuity (PVAN) on the left-hand side of the equation. Also, using the PVIFA formula from the previous lesson, we calculate the interest factor to be 166.79. The formula now becomes:

$150,000 = PMT × (166.79)

To solve for the monthly PMT, we divide each side by 166.79.

That is, $899.33 = PMT, or the monthly mortgage payment on the loan. This monthly payment includes portions that go toward interest and principal repayment over time.

Now, look at the same mortgage loan with three different interest rates.

think about it

What do you notice?

Mortgage Amount	Interest rate (r)	Monthly Payment
$150,000	3%	$632.41
$150,000	6%	$899.33
$150,000	10%	$1,316.36

key concept

You can clearly see that when the interest rate increases, the monthly payment increases for the same mortgage of $150,000. This is why understanding the concepts in this lesson is so helpful when saving for a down payment on a house, college, or retirement. Essentially, a plan to make regular savings deposits to achieve a goal or receive retirement payments is like an annuity.

try it

Calculating the Loan Amount of a Mortgage

After you figure this out, check if you are correct by selecting the “+” icon to reveal the answer.

Olawale is borrowing money to purchase a home, and his annual payment amount is $19,143.89, which will be split into 12 payments a year. If Olawale is obtaining a 30-year mortgage with a 6.5% annual interest rate, what will be the total amount of his mortgage? The is 13.059.

The total mortgage amount is the PV of his payments over 30 years. To find the loan amount, use the following formula and solve for PVAN:
PVAN = PMT × ()
PVAN = $19,143.89 × 13.059 = $250,000.00.

The amount of Olawale’s mortgage is $250,000.00.

For reference, the PVAN and FVAN formulas can be used to calculate:

1. How much is needed to deposit each period to reach a SMART goal
2. How a different interest rate (r) would affect the total amount saved or paid
3. How long it will take to reach a financial goal
4. What end goal you will achieve by setting aside savings or making payments over specified periods (t)
5. What the value is today of receiving periodic payments over a set number of future time periods

It is also common in financial planning to calculate the FV of a series of cash flows (FVAN) when saving for a goal, such as saving for college, a down payment on a house, or retirement. Does this sound familiar? These regular deposits are an annuity, so we can use the annuity formulas to answer our questions. Let’s look at another life goal: putting money into a retirement account.

1b. Saving for Retirement

What if you want to have $1,000,000 (the FV) in the bank when you retire? If your bank is currently paying a 3% interest rate (r) compounded annually, and you feel that you can save $10,000 per year (PMT) to put into a retirement account, what will you have in your account at age 65 if you start saving at age 25?

Use the FVAN formula to answer this question:

Using the FVIFA formula from the previous lesson, we calculate the interest factor to be 75.401. The formula now becomes:

FVAN = $10,000 × (75.401)

FVAN = $754,010

At the end of 40 years, you will have $754,010. In this case, you will fall short of your goal. However, if you can earn 5%, you can exceed your goal.

Using the FVIFA formula from the previous lesson, we find the interest factor to be 120.800. The formula now becomes:

FVAN = $10,000 × (120.800)

FVAN = $1,208,000

try it

Calculating How Much to Save Annually to Reach a Goal

After you figure this out, check if you are correct by selecting the “+” icon to reveal the answer.

You would like to have $500,000 in 20 years and start with no money. If you can earn a 7% annual rate of return, how much do you need to save each year in order to reach your goal? The is 40.995.

To find the annual amount, use the following formula and solve for PMT:

Help With the Calculations

There are many personal finance software packages and free resources on the Internet. You can find a mortgage calculator, a loan calculator, or a retirement planner to answer questions such as “How much do I have to save every year for retirement?” or “What will my monthly loan payment be?” Most importantly, be sure to use reputable sites and be careful not to give out any personal information online unless you have officially verified the source.

learn more

You can try one of the free financial calculators at www.dinkytown.net. Remember, never give personal information, and use the site as a resource for beginning to understand your options. Always check with a financial professional, such as an employee at your bank, before completing any financial application or sharing personal information.

The same formula can be used to calculate how much needs to be saved to pay off debt, such as a mortgage, save for a down payment on a home, or save money for college tuition.

1c. Saving for College Tuition

Adelina
A mother wanting to finish her degree

Now, let’s look at Adelina, who has saved $1,000 and wants to save more for her college tuition in the short term and the down payment on a home in the long term. If college tuition costs $130 per credit hour and Adelina needs 124 credits for her degree but has only completed 74 credits, she will need to complete 50 more credits. The estimated cost of finishing her degree is $130 × 50 credits or $6,500, minus the $1,000 she’s already saved. Since Adelina’s youngest son is only 2 years old, she plans to wait until her son is 6 before returning to college. Adelina is earning 5% on her savings account, so using our FVAN formula, we can solve for the PMT to see how much Adelina needs to save each year to achieve her goal:

Using the FVIFA formula from the previous lesson, we calculate the interest factor to be 4.310. The formula now becomes:

$5,500 = PMT × (4.310)

$1,276.10 = PMT

Thus, Adelina will need to save $1,276.10 per year to meet her goal.

try it

Calculating How Much to Save Annually for College Expenses

After you figure this out, check if you are correct by selecting the “+” icon to reveal the answer.

Your daughter is 2 years old, and you would like to save $50,000 by the time she is 18 years old for her college expenses. If you can earn a 5% annual rate of return, how much will you need to save each year in order to reach your goal? The is 23.657.

To find the annual amount, use the following formula and solve for PMT:

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2. Assessing the Impact on Your Budget

You now see the benefit of using the PVAN and FVAN formulas to determine monthly payments for college, a mortgage, or other expenditures. However, this information is only helpful if you understand how these cash flows relate to your budget.

EXAMPLE

Suppose you calculate a monthly mortgage payment of $899.50 on a loan for $150,000, but you only have a budget surplus of $500. Using the mortgage loan payment calculated, you should go back to your budget to see if your goal is realistic. To become a homeowner, you may need to eliminate unnecessary expenses to meet the new mortgage payment.

However, don’t forget that owning a home is more expensive than just the mortgage payment. Creating a projected budget based on what you would like to do, such as buying a home, and adding in the extra expenses of real estate taxes, utilities, and mortgage are extremely beneficial in seeing the full impact of home ownership on your budget. Creating a projected or estimated new budget is a smart way to see if you can truly carry the added expenses of your goal beforehand. Projected financial statements, called pro forma statements, are used in financial planning to see the expected changes in your income, expenses, or wealth depending on your potential choices. Pro forma statements allow you to get a glimpse into your projected income statement and balance sheet for any choice you consider. When making personal financial decisions, it is vital to think about their consequences on your financial statements and wealth accumulation to avoid negative consequences.

term to know

Pro Forma Statements

Projected financial statements based on expected changes in your income, expenses, asset ownership, or otherwise.

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3. Realistic Strategies for Setting Short-Term Goals to Meet Long-Term Goals

think about it

Sometimes, a big goal can be overwhelming, or you may not see a path toward a long-term goal because it is too far away. You may not be motivated and feel discouraged. You are not alone. Most people experience this feeling when they think about saving for retirement or purchasing a home when all their income goes to paying living expenses with no cash left over to save.

This is when financial planning becomes even more critical. As you discovered, creating a budget to see where your money goes and reviewing each expense to determine if they are necessary is the first step. Next, finding a reasonable way to begin saving is the second step toward feeling like you can make changes and progress toward financial goals.

Establishing a small and realistic short-term goal, such as setting aside $10 a week, will help you see your progress and money grow, which gives you a confidence boost. Here are a few suggestions to get started toward achieving your short-term goals that can help you move on to bigger, long-term goals later:

• Temporarily lease a smaller apartment to save money for a down payment on a home.
• Lease a car for 2 to 3 years to save money for a car purchase.
• Buy a used car that is 2 or 3 years old instead of a new car to lower your monthly expenses and begin saving money for retirement.
• Keep your car for a few more years to save on a car payment if it does not need expensive repairs.
• Set aside a small amount of money into a special account each week for a wedding. Keeping your savings separate avoids the temptation to spend it.
• Work a second job on weekends or over the holidays when part-time labor is needed to earn extra money and accomplish a short-term goal.
• Drive you and your family to a vacation destination instead of flying. Grill and make a fun family meal instead of eating out every night.
• Explore vacation rentals to reduce hotel costs and save money by eating in.
• Choose a lower-cost vacation, such as staying at a park or a lower-cost hotel, instead of going all out and staying at a five-star resort.
• Plan to eat out only once a week or twice a month as a reward to save money instead of spending your hard-earned pay on eating out four or five times a week.
• Have an amount automatically deducted from your pay and placed in a savings account to be used for making annual IRA contributions. This is especially important as a young adult when you won’t miss the extra cash and before you become accustomed to a more expensive lifestyle.

These are just a few options that will help you achieve your short-term goals that can help you make progress toward long-term goals.