How would you go about solving this problem and what formula am I suppose to use?

Question

Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 8%/year compounded monthly. If the future value of the annuity after 14 yr is $70,000, what was the size of each payment? (Round your answer to the nearest cent.)

Answer 1

You actually need to use two formulas. First, you need to find the period interest rate, i= r/m, where r is the nominal interest rate and m is the number of compounding periods per year. In this case, the nominal annual interest rate is 8% and the month period interest rate is 8% divided by 12 months, since there are 12 months in a year. i= 8/12= 0.67%.

 

 

Use the formula: F= A[(1+i)^n-1]/i  , where F is the future value=70000, A is the annuity, i is the period interest rate=0.67%, n is the number of periods= 12* 14= 168

 

70000= A [(1+0.0067)^168-1]/0.0067

Rearranging the equation, you will find that A=226.51

 

For future reference, if you need to check your answers you can search for a finance calculator online- in this case you would plug in F, i and n into the calculator and it will tell you what A is.