Question

06: An annuity due pays an initial benefit of 1 per year, with the benefit increasing by 10.25% every four years. The annuity is payable for 40 annual payments. Using an annual effective rate of 2%, calculate the future value of this annuity A) 42 B)69 C)83 D) 59 E) 93

Answer 1

Let us first understand the cashflows structure and increment

1035 PV2 PV. h-

1 O 之 1a
let us calculate FV i.e. future value of $2 for 4 years

We know that r = 2% per annum

FV for annuity due =(1+r)* ((1+r)^4-1)/r = 4.204

Now FV1=FV2=FV3=FV4=.........FV10=4.204

now since aur FVs are standing at 4 year's distance then our interest rate should also have for year compounding frequency that rate is R(4) = (1+r)^4 -1 = 1.02^4 -1= 8.243%

Know since our FVs are growing at the rate of 10.25 % per 4 year then we need to calculate a co- growth interest rate = which is given by

R* = ((1+g)*(1+R(4))) -1 = (1.1025 *1.08243 ) -1 = 19.34%

Now our final Future value is

= ((1+R*)^10 -1)/R* × (1/(1 +g) = (1.1934^10 -1)/.1934 ×(1/(1.1025) =95.81 $

The closest option is d 93$