Question

By the end of this year you would be 35 years old and you want to plan for your retirement. You wish to retire at the age of 65 and you expect to live 20 years after retirement. Upon retirement you wish to have an annual sum of $50,000 to supplement your social security benefits. Therefore, you opened now your retirement account with 7% annual interest rate. At retirement you liquidate your account and use the funds to buy an investment grade bond which makes $50,000 annual coupon payments based on a 6 % coupon rate, throughout your retirement years.

Please calculate the monthly payment in your retirement account in order to be able to achieve the plan mentioned above?

Answer 1

Calculation of Amount required for savings:

P = Annual Coupon payments = $50,000

n = 20 years

r = coupon rate = 6%

Amount needed at retirement = P * [1 - (1+r)^-n] / r

= $50,000 * [1 - (1+6%)^-20] / 6%

= $50,000 * 0.688195273 / 0.06

= $573,496.062

Therefore, amount required at retirement = $573,496.06

Calculation of Monthly contribution to retirement account

n = 30*12 = 360 months

r = monthly interest rate = 7%/12 = 0.5833333333%

P = Monthly contribution

PV = Amount required at retirement

Monthly contribution can be calculated using the below formula

PV = P * [(1+r)^n - 1] / r

$573,496.06 = P * [(1+0.5833333333%)^360 - 1] / 0.5833333333%

$3,345.39368 = P * 7.11648779

P = $470.090552

Therefore, monthly contributio inorder to achieve the plan is $470.09