A fund pays 1 at time t = 0, 2 at time t = 2n and 1 at time t = 4n. The
present value of the payments is 3.61. Calculate $(1 + i)^n$.

Hi Markgvanzalk,

Here is a detailed solution:

When solving for the interest rate, the payments are discounted back to time t = 0, where the present value is 3.61.

The formula to calculate the future value is :
FV = PV * (1+i)^n

So,

3.61 = 1/(1+i)^0 + 2/(1+i)^2n + 1/(1+i)^4n

Assuming (1+i)^2n = X, we have:

3.61 = (1/1) + (2/X) + (1/X^2)

So,

2.61 X^2 = 2X+1

Solving for X, we get X = 1.11

So, we get (1+i)^n = sqrt(1.11) = 1.05409


If you liked the details answer provide, a tip is appreciated. Thanks.

Best,
Kav10