How much would I have to deposit

Question

Determine how much you would have to deposit into a CD that was paying 2.75% simple interest annually if you wanted to have $10980 in the account after 8 years. 

 

B) calculate the rate of return on this investment.

 

awser of A: $9000.00

awser of B: 22%

 

~I can't find the way to do it.

Answer 1

The formula for simple interest is I = P*R*T where 

 

I = amount of Interest earned

P = Principal or original deposit 

R = interest Rate as a decimal

T = Time, normally in years 

 

You want the total amount (which is principal plus interest) to be $10980 so 

 

P + I = 10980

P + P*R*T = 10980

P(1 + R*T) = 10980

P = 10980 / (1 + R*T)

 

Now plug in the values R = 0.0275 and T = 8 

 

P = 10980 / (1 + 0.0275*8)

P = 10980 / (1 + 0.22)

P = 10980 / 1.22

P = $9000  is the original deposit 

 

So the total interest earned is I = 10980 - 9000 = 1980 

 

The rate of return is I/P = 1980 / 9000 = 0.22 = 22% 

 

Note that 22% (total return)= 2.75%(annual return) * 8 (years)