Question

At an annual effective interest rate of 10.9%, each of the following are equal to X:

The accumulated value at the end of n years of an n-year annuity-immediate
paying 21.80 per year.
• The present value of a perpetuity-immediate paying 19, 208 at the end of each
n-year period.
Calculate X .

Answer 1

FIRST ANNUITY

The accumulated Value =
`P[((1+r)^(n) - 1)/(r)] * (1+r)`

The accumulated Value =
`21.80[((1.109)^(n) - 1)/(0.109)] * (1.109)`

SECOND CASH-FLOW

We can simply calculate our answer by evaluating the perpetuity as no variable is missing. Hence,

The Present Value =
`192.8 + (192.8)/(0.109)`

The Present Value = 192.8 + 1768.8

The Present Value = 1961.61

As per the question :

`192.8 + (192.8)/(0.109)` =
`21.80[((1.109)^(n) - 1)/(0.109)] * (1.109)`

Hence, second expression is also approx equal to $1960.