A selfemployed person has a Keogh retirement plan This type

A self-employed person has a Keogh retirement plan. (This type of plan is free of taxes until money is withdrawn.) If deposits of $7500 are made each year into an account paying 8% compounded annually, how much will be in the account after 20 years?

Sun America offered an annuity that pays 6.35% compounded monthly. What equal monthly deposit should be made into this annuity in order to have $200,000 in 15 years?

Solution

a)Future Value = P[(1 + i)^n - 1]/i

Future value = 7500[(1 + 0.08)^20 - 1]/0.08
Future value = $343,214.73
b) Let R = 1+.0635/12

Future value= p * [{1+rate)^(no. of periods+1) - 1}/{ rate}

no of months in 15 yrs = 180

200000 = p * [(R^181-1)/(R-1)]

So p= 200,000/[(R^181 - 1)/(R-1)]

= 200,000/[1.5993630/.00529167]

= $661.72 p.m