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Question 1159853: To buy a laptop computer, Aline wants to borrow $2000 for 3 years. She lives near two banks.
The first bank offers the amount with a 5% simple interest rate.
2. Compute the future value.
The second bank offer the amount with a 6% interest rate compounded annually.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! simple interest formula is f = p * (1 + r * t)
p is the present value
f is the future value
r is the interest rate per time period
t is the number of time periods
at 5% simple interest rate with p = 2000 for 3 years, the formula becomes:
f = 2000 * (1 + .05 * 3) = 2000 * (1 + .15) = 2000 * 1.15 = 2300.
compound interest formula is f = p * (1 + r) ^ n
p is the present value
f is the future value
r is the interest rate per time period
n is the number of time periods
at 6% interest rate compounded annually, with p = 2000 and n = 3, the formula becomes:
f = 2000 * (1 + .06) ^ 3 = 2000 * 1.06^3 = 2000 * 1.191016 = 2382.032.
the second bank costs her more for two reasons.
1) the interest rate per year is higher.
2) compound interest rate formula leads to a higher future value then simple interest rate formula, even with the same interest rate.
for example, assuming the interest rate was 5% for both, the future value with simple interest rate formula is 2300.
the future value with compound interest rate formula at the same rate of 5% per year would be f = 2000 * (1 + .05) ^ 3 = 2000 * 1.05 ^ 3 = 2000 * 1.157625 = 2315.25
the compound interest rate formula gets you a higher future value because the bank is earning interest on the interest earned during the previous year, whereas the simple interest rate formula earns you interest only on the original principal.
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