Question

An individual wants to accumulate $750,000 for retirement in 30 years. She wants to make yearly deposits into an account which earns 8% annually. Determine the size of the payments needed if the payments are made at: A: the end of the year. ($6620.58) B: the beginning of each year. ($6130.16) Cannot use Excel.

Answer 1

Required Future Value to accumulate (FV)= 750000

Interest rate (I)= 8%

Number of years (n)= 30

A.

Payment is to be made at end of Year, so it is ordinary Annuity.

Amount required to save each period at end (ordinary Annuity) to accumulate Future Value Formula = Future value*i/(((1+i)^n)-1)

=750000*8%/(((1+8%)^30)-1)

=6620.57504

So Amount Required to save each year at end is $6620.58

B.

Payment is to be made at Beginning of Year, so it is Annuity due.

Amount required to save each period at Beginning (Annuity due) to accumulate Future Value Formula = Future value*i/((((1+i)^n)-1)*(1+i))

=750000*8%/((((1+8%)^30)-1)*(1+8%))

=6130.162074

So Amount Required to save each year at Beginning is $6130.16