Question

5. What is the present value of $100 per month at a discount rate of 6%, if the
first payment is received 5 years from now and the last payment is received 18 years from
now?

Could you explain in detail with formula plz!

Answer 1

First let us know the present value of payments at the beginning of 5 th year.

=> A*[1-(1+r)^(-n)]/r

here,

A=100

r=6%

r = 6%*1/12

=>0.5%=>0.005.

n = 5 th year to 18 th year

=>14 years*12 months =>168.

present value of annuity =100*[1-(1.005)^(-168)]/0.005

=>100*113.477

=>$11,347.70.

This is the value at the beginning of 5 th year.

So the present value will be = amount at beginning of 5th year / (1+r)^n

here ,

r=0.005

n = 4 years * 12 months

=>48.

=>$11,347.70 / (1.005)^48

=>$8,931.76.