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

Answer:

FIRST ANNUITY

The accumulated Value = $P[\frac{(1+r)^{n} - 1}{r}] * (1+r)$

The accumulated Value = $21.80[\frac{(1.109)^{n} - 1}{0.109}] * (1.109)$

SECOND CASH-FLOW

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

The Present Value = $192.8 + \frac{192.8}{0.109}$

The Present Value = 192.8 + 1768.8

The Present Value = 1961.61

As per the question :

$192.8 + \frac{192.8}{0.109}$ = $21.80[\frac{(1.109)^{n} - 1}{0.109}] * (1.109)$

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