) Your family member wants some advice. In 20 years, they plan to retire and the

Question

) Your family member wants some advice. In 20 years, they plan to retire and they would like to have 3 $300,000 saved up. Th for the first 10 years only. How much do they need to deposit each year in an account at 10% interest in order to have met their savings goal? ey want to deposit the same amount of money each year at the end of the year a. $5,740 b. $7,285 c. $7,550 d. $8,040 12) You loaned a person $500 and you said that you would charge him 15% annual interest. If you get paid back, $110 per year, how many years will it take to pay this off? a. 5-6 years b. 6-7 years c. 7-8 years d. 8-9 years

Explanation / Answer

(11) Option (b)

If required annual savings for 10 years be S, then

S x F/A(10%, 10) x F/P(10%, 10) = $300,000

S x 15.9374** x 2.5937** = $300,000

S x 41.3375 = $300,000

S = $7,257 [The slight difference is due to rounding off]

**From F/A and F/P factor tables

(12) Option (d)

Annual loan repayment ($) = Loan amount / P/A(15%, N)

$110 = $500 / P/A(15%, N)

P/A(15%, N) = 4.5454

[1 - (1.15)-N] / 0.15** = 4.5454

[1 - (1.15)-N] = 0.6818

(1.15)-N = 0.3182

(1.15)N = 3.1429

Taking natural logarithm on both sides,

N x ln 1.15 = ln 3.1429

N x 0.1398 = 1.1451

N = 8.19

**P/A(r%, N) = [1 - (1 + r)-N] / r

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