Question

John won a lottery that will pay him $500,000 at the end of each of the next twenty years. Assuming an appropriate interest rate is 8% compounded annually, what is the present value of this amount?

Assume ABC Company deposits $90,000 with First National Bank in an account earning interest at 6% per annum, compounded semi-annually. How much will ABC have in the account after five years if interest is reinvested?

Lucy and Fred want to begin saving for their baby's college education. They estimate that they will need $120,000 in eighteen years. If they are able to earn 5% per annum, how much must be deposited at the end of each of the next eighteen years to fund the education?

		$4,648.
		$10,266.
		$9,929.
		$4,266.

Answer 1

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$500,000[1-(1.08)^20]/0.08

=$500,000*9.818147407

=$4909073.70(Approx).

2.We use the formula:
A=P(1+r/200)^2n
where
A=future value
P=present value
r=rate of interest
n=time period.

A=$90000(1+0.06/2)^(2*5)

=$90000*1.343916379

=$120,952.47

3.

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

120,000=Annuity[(1.05)^18-1]/0.05

120,000=Annuity*28.13238467

Annuity=120,000/28.13238467

which is equal to

=$4266(Approx).