Question

Simple versus compound interest

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.