Question

How much more money is required to fund an ordinary perpetuity than a 15-year ordinary annuity, if the funds can earn 5% compounded quarterly, and both pay $600 monthly? (Do not round intermediate calculations and round your final answer to 2 decimal places.)
$ more money is needed to fund the perpetuity

PLEASE IM EXPECTING A CORRECT ANSWER FROM YOU

Answer 1

For an ordinary perpetuity, it will pay for the lifetime.

monthly payment = $600

interest rate = 5% compounded quarterly

First calculating monthly rate

So, effective annual rate EAR = (1 + quarterly rate/n)^n - 1

For quarterly compounding, n = 4

So, EAR = (1 + 0.05/4)^4 - 1 = 5.09%

for monthly rate, r = (1+EAR)^(1/n), where n = 12 months in a year

So, monthly rate r = (1+0.0509)^(1/12) - 1 = 0.4149%

So, value of ordinary perpetuity = monthly payment/monthly rate = 600/0.004149 = $144598.34

For a 15 year ordinary annuity, it value is calculated using formula

PV = PMT*(1 - (1+r)^(-n*t))/r = 600*(1 - (1+0.004149)^(-12*15))/0.004149 = $75976.65

So, extra money needed to fund perpetuity = value of perpetuity - value of annuity = 144598.34 - 75976.65 = $68621.69