Question

You are given:

a. The present value of a perpetuity of 100 per year, the first payment at the end of n years, is 169.
b. The present value of an increasing perpetuity of 100, 200, 300, etc., the first payment at the end of n years, is 2,112.50.
c. The annual effective interest rate is i.

Required:
Calculate i.

Answer 1

0.087 = 8.7%

Step-by-step explanation:

Present value of perpetuity given that payment is done at the end of N-year

= present value * ( 1 + i )^n-1

= 169 * ( 1 + i )^n-1 = 100 / i

∴ ( 1 + i )^n-1 = 100 / 169i ------- ( 1 )

Given that first payment at the end of N years = 2112.50 hence the present value of 2112.50

= 2112.50( 1 + i )^n-1 = 100 / i + 100/ i^2 --- ( 2 )

(given that the increment is with a difference of 100 ) and N-1 = number of years

next step : Input equation 1 into equation 2

2112.50 i^2 = 169i [ 100i + 100 ]

19350 i^2 = 16900i

∴ i = 16900 / 19350 = 0.086956 ≈ 0.087