Question

An investor makes three deposits into a fund, at the end of 1, 3, and 5 years. The amount of the deposit at time t is 100(1.025)t . Find the size of the fund at the end of 7 years, if the nominal rate of discount convertible quarterly is 4 41 .

Answer 1

The size of the fund at the end of 7 years is $483.110

Step-by-step explanation:

Number of quarters = 4

We are given that the nominal rate of discount convertible quarterly is 4/41

Discount rate in each quarter =
`((4)/(41))/(4) = (1)/(41).`

Let A is the value after discount and X is the original value:

`A = X - X((1)/(41)) \\A=X(1 - (1)/(41)) \\A=(40)/(41)X\\X = (41)/(40)A`

Now To calculate the value after 7 years we need to multiply each value by the interest raised to the correct power.

`A=100 * 1.025^1 * (41)/(40)^((7-1) * 4)+100 * 1.025^3 * (41)/(40)^((7-3) * 4)+100 * 1.025^5 * (41)/(40)^((7-5) * 4)`

A=483.110

Hence the size of the fund at the end of 7 years is $483.110