Question

Manulife Investment Company intends to offer a guaranteed annuity in units of RM800, payable at the end of each year for 20 years. The company has a strong investment record and can consistently earn 7 percent on its net investments after taxes.

Required:

If the company intends to earn 1 percent on this contract, compute the estimated price that Manulife should set, with a 6 percent discount rate.

Answer 1

Sol:

Annuity value/Cash flows (CF) = RM800

Period (n) = 20 years

Interest rate (r) = 7% (Company intends to earn 1 percent on this contract), therefore discounted annuity value will be at 7% - 1% = 6%

Present value of annuity = PV

To determine the estimated price that company should set:

PV = CF x (1 - (1/(1+r)n)/r

PV = 800 x (1- (1/(1+6%)^20)/6%

PV = 800 x (1- (1/(1+0.06)^20)/0.06

PV = 800 x (1- (1/(1.06)^20)/0.06

PV = 800 x 11.4699

PV = RM9175.94

Therefore estimated price that company should set will be RM9175.94

Alternatively you can also use the PV function in excel =PV(6%,20,800,0) to get the estimated price that company should set.