Question #171021

QUESTION 1

(a). Suppose you make an investment of K1,000. This first year the investment returns 12%, the second year it returns 6%, and the third year it returns 8%. How much would this investment be worth, assuming no withdrawals are made?

(b). Congratulations! You have just won a small lottery. It will pay you either 5 annual payments of K15,000 each (with the first payment to be received one year from today), or a single lump sum to be received today. If you can invest at a 6% annual rate of interest, what is the least you should accept as the lump sum payout amount?

(c). Suppose an annuity costs K40,000 and produces cash flows of K10,000 over each of the following eight years. What is the rate of return on the annuity?

(d). How long does it take for your money to grow to ten times its original value if the interest rate is 5% per year?

Expert's answer

(a)

"FV=PV(1+r1)^1(1+r2)^2(1+r3)^3=1000(1+0.12)^1(1+0.06)^2(1+0.08)^3=1585.26"

(b) FV=15000

r=0.06

n=1

"FV=PV(1+r)^n"

"15000=PV(1+0.06)^1"

PV=14 150.94

(c)"FV=A\\frac{(1+r)^n-1}{r}"

"40000=10000\\frac{(1+r)^8-1}{r}"

"4=\\frac{(1+r)^8-1}{r}"

"4=\\frac{(r)^8}{r}"

"4=r^7"

r=1.22

(d) Let

FV=800, PV=80

"n=\\frac{log(\\frac{FV}{PV})}{log(1+r)}=\\frac{log(\\frac{800}{80})}{log(1+0.08)}=\\frac{1}{0.03342}=29.92"

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