Question

Brian deposited $8,074 into a savings account for which interest is compoundeddaily at a rate of 2.66%. How much interest will he earn after 6 years? Round answerto the hundredths place. If answer does not have a hundredths placethen includezeros so it does.

Answer 1

The compound interest formula for the amount of money A in an account after t years if a principal P is invested at an annual interest rate r (as a decimal) in n compounding periods a year is:

`A=P(1+(r)/(n))^(nt)`

In this case, the principal P is equal to 8074, the rate of 2.66% as a decimal is r=0.0266, the number of compounding periods a year is 365 and the time is equal to 6 years. Then, replace P=8074, r=0.0266, n=365 and t=6 to find the amount in the account after 6 years:

`A=8074*(1+(0.0266)/(365))^(365*6)=9471.082482...`

Subtract from the amount A the principal P to find how much interest will the account earn:

`9471.082482...-8074=1397.082482...\approx1397.08`

Therefore, to the nearest hundredth, the amount of interest that the account will earn is $1397.08.