Question

Tracy opened a savings account and deposited $600.00. The account earns 4% interest,compounded annually. If she wants to use the money to buy a new bicycle in 3 years, howmuch will she be able to spend on the bike?Round your answer to the nearest cent.

Answer 1

The compound interest formula is:

`C(n)=P\lbrack(1+i)^n-1\rbrack`

Where:

C(n) is the interest generated after n periods

P is the principal value, the values deposited initially.

i is the annual interest rate in percentage terms.

n is the number of compounding periods.

In this case:

P = $600.00

i = 0.04 (converted from percentage to decimal by dividing by 100

n = 3 years

Then:

`C(3)=600.00\lbrack(1+0.04)^3-1\rbrack`

Then solve:

`C(3)=600\lbrack1.04^3-1\rbrack=600\lbrack1.124864-1\rbrack=600\cdot0.124864=74.9184`

This is the amount of interest generated over 3 years. The total amount then will be the initial amount plus the interest generated:

`600+74.9184=674.9184`

Rounded up to the nearest cent, the amount she will be able to spend after 3 years is $674.91