$9000 for 3 years at 7.5% compounded monthly The total amount accumulated after 33 years is

Question

Use the compound interest formula to compute the total amount accumulated and the interest earned.

Answer 1

The compound interest formula is written: 

 

 

A(t) = A_o(1+r/n)^nt

 

A₀= initial amount (in our case unknown) 

r = rate expressed as a decimal (in this case it's .075) 

n = number of times the interest is compounded each year (in our case 12).

t = the time in years.

 

 

A(t)=A_o(1+.075/12)^{12t                                (1)} 

 

We do not know the initial amount A_o in equation (1) but we do know the amount after 3-years, which is $9000. This means A(3)=9000

 

So set t=3 in equation (1) and then solve for the initial amount: 

 

 

A(3) =$9000 =A_o(1.00625)¹²⁽³⁾

 

Divide to find the initial amount. I find that A_o =$7191

 

So now we can update equation (1). 

 

A(t)=$7191(1.00625)^12t

 

Now find the amount after 33 years by evaluating A(33)

 

A(33)=$7191(1.00625)¹²⁽³³⁾ = $84785

 

So about $84785