Question

1. a) You have won a lottery. Lottery officials offer you the choice of the following alternative payout: Alternative 1: $300,000 two years from now. Alternative 2: $950,000 four years from now. What discount rate makes the two alternatives equally attractive to you?
b) You have $11,000 in an account earning 15% interest per annum. How large annuity can you draw out each year if you want nothing left at the end of 5years?
c) Stanbic Bank pays 12% per annum simple interest on its savings account balance and SG Bank pays 12% per annum interest compounded weekly. If you made a $14,000 deposit in each bank, how much more money would you earn from SG account over Stanbic Bank account at the end of 3years?
d) You invested in a mutual fund that offers 12% interest per annum. How long will it take your investment of $350,000 to grow to $2million?

Answer 1

a) $\frac{300,000}{(1+r)^2}=\frac{950,000}{(1+r)^4}$

$r=0.4685=46.85$

b) $11,000*1.15^5-x*\frac{1.15^5-1}{1.15-1}=0$

$x=3,281.47$

c) $14,000*(1+\frac{0.12}{52})^{52*3}-14,000*(1+0.12*3)=1,018.29$ you will earn more money  from SG account over Stanbic Bank account

d) $350,000*1.12^n=2,000,000$

$n=15.38=15 \ years \ 5\ months$