A company deposits $1000 every year for ten years in a bank. The company makes n

Question

A company deposits $1000 every year for ten years in a bank. The company makes no deposits during the subsequent five years. If the bank pays 8% interest, the amount in the account at the end of 15 years is nearest to $10,800 15,000 16,200 21, 200 $25,000 is deposited in a savings account that pays 5% interest, compounded semiannually. Equal annual withdrawals are to be made from the account, beginning one year from now and continuing forever. The maximum amount of the equal annual withdrawal is closest to $625 1000 1200 1265 1365 What present sum would need to be put in a savings account now to provide a $1000 annual withdrawal for the next 50 years, if interest is 6%? The present sum is closest to: $1,000 10,000 25,000 37,500 50,000

Explanation / Answer

(14) (d)

Future value (FV) after 10 years ($) = 1000 x FVIFA(8%, 10) = 1000 x 14.4866 = 14,487

Compounded to next 5 years, FV at end of 15 years ($) = 14,487 x FVIF(8%, 5) = 14,487 x 1.4693 = 21,286

(15) (e)

Semi-annual interest rate = 5% / 2 = 2.5%

Number of compounding periods = 2

FV after 1 year ($) = 25,000 x FVIF(2.5%, 2) = 25,000 x 1.0506 = 26,265.63

If maximum withdrawal be A, then

26,265.63 = A / 0.05

A = 26,265.63 x 0.05 = 1,313.28

(16) (b)

Required sum ($) = 1000 x PVIFA(6%, 50) = 1000 x 15.7619 = 15,762

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