Question

Simple versus compound interest

Financial contracts involving investments, mortgages, loans, and so on are based on either a fixed or a variable interest rate. Assume that fixed interest rates are used throughout this question.

Zoe deposited $900 in a savings account at her bank. Her account will earn an annual simple interest rate of 7%. If she makes no additional deposits or withdrawals, how much money will she have in her account in thirteen years?

a. $1,719.00

b. $2,168.86

c. $967.41

d. $163.00

Now, assume that Zoe's savings institution modifies the terms of her account and agrees to pay 7% in compound interest on her $900 balance. All other things being equal, how much money will Zoe have in her account in thirteen years?

a. $963.00

b. $151.82

c. $2,168.86

d. $1,719.00

Suppose Zoe had deposited another $900 into a savings account at a second bank at the same time. The second bank also pays a nominal (or stated) interest rate of 7% but with quarterly compounding. Keeping everything else constant, how much money will Zoe have in her account at this bank in thirteen years?

a. $166.16

b. $964.67

c. $163.00

d. $2,218.36

Answer 1

Answer:

The correct answers are a. $1719.00 ; c. 2168.86 ; d. $2218.36.

Explanation:

Zoe deposited $900 in a savings account at her bank.

Her account will earn an annual simple interest rate of 7%.

Time for which the money is deposited for 13 years.

Money Zoe would have in her account in thirteen years  is

Principal + Principal × time × $\frac{interest rate}{100}$ = 900 + 9 × 13 ×7 = 900 + 819 = $1719

Now, assume that Zoe's savings institution modifies the terms of her account and agrees to pay 7% in compound interest on her $900 balance.

Money Zoe would have in her account in thirteen years  is

Principal × $(1 + \frac{interest rate}{100}) ^{time}$ = 900 × $( 1 + \frac{7}{100} )^{13}$ = $2168.86.

Suppose Zoe had deposited another $900 into a savings account at a second bank at the same time. The second bank also pays a nominal (or stated) interest rate of 7% but with quarterly compounding.

Time has now changed to 4× 13 = 52.

Money Zoe would have in her account in thirteen years  is

Principal × $(1 + \frac{interest rate}{100}) ^{time}$ = 900 × $( 1 + \frac{7}{400} )^{52}$ = $2218.36.