Question

how much jim can accumulate in a private pension fund over 20 years if the fund offers 5% interest compounded annually, and he can afford to deposit $2 000 at the end of every second year?

Answer 1

Jim can accumulate approximately $35,566.06 in his private pension fund over 20 years. This is based on making $2,000 deposits at the end of every second year with a 5% annual compound interest rate

To calculate the future value of Jim's pension fund, where he deposits $2,000 at the end of every second year with a 5% annual compound interest rate over 20 years, we'll need to treat it as a series of individual future value calculations. This is because each deposit will have a different amount of time to grow.

Here's the step-by-step approach:

1. Individual Deposit Growth Calculation : Each deposit will grow at 5% annually until the end of the 20-year period. The future value \( FV \) of each deposit is given by the formula:

`\[ FV = P * (1 + r)^t \]`

where
`\( P \)` is the deposit amount ($2,000),
`\( r \)` is the annual interest rate (5% or 0.05), and
`\( t \)` is the number of years each deposit grows.

2. Calculate Growth for Each Deposit : Jim makes a deposit every two years, so the first deposit will grow for 20 years, the second for 18 years, and so on until the last deposit, which will grow for 2 years.

3. Sum the Future Values of All Deposits : Add the future values of all the deposits to get the total amount accumulated in the pension fund after 20 years.

Jim can accumulate approximately $35,566.06 in his private pension fund over 20 years. This is based on making $2,000 deposits at the end of every second year with a 5% annual compound interest rate. The calculation takes into account the different growth periods for each deposit, as earlier deposits have more time to accumulate interest than later ones.