Question

Suppose an investor plans to make monthly deposits into an account that pays 9% interest, compounded monthly, so that $100,000 will be in the account immediately after the payment at the end of Year 10. The first payment will occur at the end of Month 1 (one month from the present). How much must be deposited monthly

Answer 1

As per the information given in the question

The interest rate of interest given by the account (r) =9% =0.09 compounded monthly

Thought the interest is compounded monthly so compounding period (M) =12 then the required monthly interest rate (i) = r/M = 0.09/12 = 0.0075 =0.75%  

Though the investor plans to make monthly deposit (A) for 10 years so the number of interest bearing period (N)= 12x10 = 120 months

Future worth of the deposit at the end of 10 year (F)= $100000

The required monthly deposit (A) = ?

A= F(A/F,i,N)

A = $100000(A/F,0.75%,120)

A=F[i/{(1+i)^N-1}]

A=$100000[0.0075/{(1+0.0075)¹²⁰-1}]

A=$100000[0.0075/{(1.0075)¹²⁰-1}]

A=$100000(0.0051675773)=$516.7577   or Approx $516.76

The required monthly deposit in that account is (A) = $516.76