Answer:
0.087 = 8.7%
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
