Darren invests $4,500 into an account that earns 5% annual interests. How much will be in the account after 10 years if the interest rate is compounded annually, quarterly, monthly, or daily? Which compounded interest rate should Darren choose?

We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.

We will use compound interest formula to solve our given problem.    

, where,

A = Final amount,

P = Principal amount,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year,

t = Time in years.

When compounded annually, :

When compounded quarterly, :

When compounded monthly, :

When compounded daily, :

Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.

for the points! : )