III. John is currently 25 years old. He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a. He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement. He expects to live up till 70 years. How much should he deposit every month into his account?
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Given:
John is currently 25 years old.
He has $10,000 saved up and wishes to deposit this into a savings account which pays him J12 = 6% p.a.
He also wishes to deposit $X every month into that account so that when he retires at 55, he can withdraw $2000 every month end to support his retirement.
To find:
How much should he deposit every month into his account?
Solution:
The future value is:
FV = 15 × 12 × 2,000 - 10,000 = 350,000.
The monthly payment is:
P = [350,000 × 0.06/12] / [(1 + 0.06/12) ^{30 × 12} - 1] = 348.43
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