Grades K-2, 3-5, 6-8, 9-12
Hands on Banking You and Money
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Suppose your brother or sister owed you $500. Would you rather have this money repaid to you right away, in one payment, or spread out over a year in four installment payments? Would it make a difference either way?
Suppose your brother or sister owed you $500. Would you rather have this money repaid to you right away, in one payment, or spread out over a year in four installment payments? Would it make a difference either way?
First, consider future value. Future value (FV) refers to the amount of money to which an investment will grow over a finite period of time at a given interest rate. Put another way, future value is the cash value of an investment at a particular time in the future. Start by considering the simplest case, a single-period investment.
Investing For a Single Period:
Suppose you invest $100 in a savings account that pays 10 percent interest per year. How much will you have in one year? You will have $110. This $110 is equal to your original principal of $100 plus $10 in interest. We say that $110 is the future value of $100 invested for one year at 10 percent, meaning that $100 today is worth $110 in one year, given that the interest rate is 10 percent.
In general, if you invest for one period at an interest rate r, your investment will grow to (1 + r) per dollar invested. In our example, r is 10 percent, so your investment grows to 1 + .10 = 1.10 dollars per dollar invested. You invested $100 in this case, so you ended up with $100 x 1.10 = $110.
Investing For More Than One Period:
Consider your $100 investment that has now grown to $110. If you keep that money in the bank, what will you have after two years, assuming the interest rate remains the same? You will earn $110 x .10 = $11 in interest after the second year, making a total of $100 + $11 = $121. This $121 is the future value of $100 in two years at 10 percent. Another way of looking at it is that one year from now, you are effectively investing $110 at 10 percent for a year. This is a single-period problem, so you will end up with $1.10 for every dollar invested, or $110 x 1.1 = $121 total.
This $121 has four parts.
The process of leaving the initial investment plus any accumulated interest in a bank for more than one period is reinvesting the interest. This process is called compounding. Compounding the interest means earning interest on interest so we call the result compound interest. With simple interest , the interest is not reinvested, so interest is earned each period is on the original principal only.
Interest on Interest
At the end of the first year, you will have $325 x (1 + .14) = $370.50 . If you reinvested this entire amount, and thereby compound the interest, you will have $370.50 x 1.14 = $422.37 at the end of the second year. The total interest you earn is thus $422.37 — 325 = $97.37. Your $325 original principal earns $325 x.14 = $45.50 in interest each year, for a two-year total of $91 in simple interest. The remaining $97.37 — 91 = $6.37 results from compounding. How much will you have in the third year?
End of Year |
Amount on Interest |
Interest Rate |
Interest Earned |
Balance |
1 |
$1,000 |
10% |
$100 |
$1100 |
2 |
1,100 |
10% |
[110] |
[1210] |
3 |
[1,210] |
10% |
[121] |
[1331] |
4 |
[1,331] |
10% |
[133.10] |
[1464.10] |
5 |
[1,464.10] |
10% |
[146.41] |
[1610.51] |
6 |
[1,610.51] |
10% |
[161.06] |
[1771.56] |
7 |
[1,771.56] |
10% |
[177.16] |
[1948.72] |
8 |
[1,948.72] |
10% |
[194.87] |
[2143.59] |
9 |
[2,143.59] |
10% |
[214.36] |
[2357.95] |
10 |
[2,357.95] |
10% |
[235.80] |
[2593.75] |
11 |
[2,593.75] |
10% |
[259.38] |
[2853.13] |
12 |
[2,853.13] |
10% |
[285.31] |
[3138.44] |
How many years did it take to double your money? [8]
Suppose you go in for an interview for a part-time job. The boss offers to pay you $50 a day for a 5-day, 10-week position OR you can earn only one cent on the first day but have your daily wage doubled every additional day you work. Which option would you take?
Additional funding for this lesson was provided by the Mortgage Bankers’ Association of America.
Grades K-2, 3-5, 6-8, 9-12
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Grades K-2, 3-5, 6-8, 9-12
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Grades 9-12
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Grades 9-12
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Grades 9-12
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