Question

3. What is the simple interest and the amount in the account if you invested$175.00 for 90 days at 8%?

Answer 1

The formula for the simple interest I after an amount P is invested for period t at a simple interest rate r is:

`I=P\cdot r\cdot t`

In this problem, the simple interest annual rate is 8% = 0.08. But the period t of the investment is

t = 90 days = 3 months = (12/4) months = (1/4) year

And the rate is:

`r=\frac{0.08}{\text{year}}=\frac{(0.08)/(4)}{\frac{\text{year}}{4}}=(0.02)/(t)`

Then, using P = 175, the interest, in dollars, is:

`I=175\cdot(0.02)/(t)\cdot t=175\cdot0.02=3.5`

And the amount A, in dollars, in the account after that period is:

`A=P+I=175+3.5=178.5`

Answers:

Simple interest: $3.50

Ammount: $178.50