7. A woman wishes to invest $5,800. She can buy savings bonds which pay simple interest at the rate of 8.5% per annum or she can start a savings account which pays compound interest at the same rate. Calculate the difference in the amounts of the two investments at the end of five years.

Answer 1

To calculate the difference in the amounts of the two investments at the end of five years, we need to calculate the amounts separately for each investment.

For the savings bonds:

Simple interest formula: A = P(1 + rt)
Where:
A = final amount
P = principal amount = $5,800
r = interest rate per period = 8.5% = 0.085
t = number of periods = 5 years

A = 5800(1 + 0.085 * 5)
A = 5800(1 + 0.425)
A = 5800(1.425)
A = $8,215

For the savings account:

Compound interest formula: A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount = $5,800
r = interest rate per period = 8.5% = 0.085
n = number of compounding periods per year (assuming it's compounded annually)
t = number of years = 5

A = 5800(1 + 0.085)^5
A = 5800(1.085)^5
A = 5800(1.498357)
A = $8,684.76

The difference in the amounts of the two investments at the end of five years is:
$8,684.76 - $8,215 = $469.76