Question

You deposit $1,300 at the end of each year into an account paying 8.6 percent interest. a. How much money will you have in the account in 24 years? b. How much will you have if you make deposits for 48 years?

Answer 1

This is a case of annuity which involves a series of payments made at regular interval of time. The formula to determine the future value of annuity is:
=(Payment)*[((1+Interest rate)^(Time period)-1)/(Interest rate)]

Part a:
Annuity payment amount is $1,300
Interest rate is 8.6%
Time period is 24 years
Substituting the values, we get;
=(1300)*[((1+8.6%)^(24)-1)/(8.6%)]
=(1300)*[((1.086)^(24)-1)/(8.6%)]
=(1300)*[(7.242955319-1)/(8.6%)]
=(1300)*[(6.242955319)/(8.6%)]
=(1300)*72.59250371
=94370.25482 or 94370.25 (Rounded to 2 decimal places)

Hence, the future value of annuity will be $94370.25

Part b:
Substituting the value of the number of years as 48 instead of 24, we get;
=(1300)*[((1+8.6%)^(48)-1)/(8.6%)]
=(1300)*[((1.086)^(48)-1)/(8.6%)]
=(1300)*[(52.46040175-1)/(8.6%)]
=(1300)*[51.46040175/(8.6%)]
=(1300)*598.3767645
=777889.7939 or 777889.79 (Rounded to 2 decimal places)

Hence, the future value of annuity will be $777889.79