Question

A company wants to have $50,000 at the beginning of each 6-month period for the next 4 1 2 years. If an annuity is set up for this purpose, how much must be invested now if the annuity earns 6.07%, compounded semiannually?

Answer 1

PV of Annuity Due = Cash flow * { { [ 1- (1+r)^-(n-1) ]/ r } + 1 }

where r is int rate per period & n is no.of periods

= $ 50,000 * { { [ 1- (1+0.03035)^-(9-1) ]/ 0.03035 } + 1 }

= $ 50,000 * { { [ 1- (1.03035)^-8 ]/ 0.03035 } + 1 }

= $ 50,000 * { { [ 1- 0.7873 ]/ 0.03035 } + 1 }

= $ 50,000 * { 8.0093 }

= $ 400,466.98

PV of Ordinary Annuity = Cash flow * { [ 1- (1+r)^-(n) ] / r }

where r is int rate per period & n is no.of periods

= $ 50,000 * [ 1- (1+0.03035)^-(9) ] / 0.03035

= $ 50,000 * [ 1- (1.03035)^-9 ]/ 0.03035

= $ 50,000 * [ 1- 0.7641 ] / 0.03035

= $ 50,000 * {7.7734 }

= $ 388,670.82