Question

10. You are 30 years old and planning to retire at age 62. You want to plan your finances for living 35 years past age 62 and then die dead broke. You determine that you will need $3000 per month for the 35 years. At age 62, you plan to go live in the tropics on the beach and live on coconuts, rum and fishing. You need to conclude your retirement savings at age 55 because all your spare money then will go to your kids education. Ignore inflation.

The question is how much money do you need to save each month between now and 55 so that you can quit contributing and have enough money for the $3000 per month starting at age 62. The expected return on your investments over the whole period is 10% per year.

Answer 1

Solution :- Interest Rate per month = ( 1 + 0.10 )^1/12 - 1 = 0.007974 = 0.7974%

Amount Required Per Month After Retirement = $3,000

Total Monthly Payments in 35 Years = 35 * 12 = 420

Now Present Value at retirement of Money Required after Retirement = $3,000 * PVAF ( 0.7974% , 420 )

= $3,000 * 120.9429

= $362,828.81

Now the Value of Money required after retirement at age of 55 = $362,828.81 / ( 1 + 0.10)⁷

= $362,828.81 * 0.51316

= $186,188.55

Now Assume the Amount we need to deposit monthly for 25 Years =

Total Deposits = 25 * 12 = 300

Rate per ,month = 0.7974%

Future Value = $186,188.55

Monthly Deposit = X

= $186,188.55 = X * FVAF ( 0.7974% , 300 )

= $186,188.55 = X * 1233.3248

X = $150.96

Therefore Monthly Deposit = $151 ( Approx )

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