BJ's goal is to have $50,000 saved at the end of Year 5. At the end of Year 2, they can add $7,500 to their savings but they want to deposit the remainder they need to reach their goal today, Year 0, as a lump sum deposit. If they can earn 4.5 percent, how much must they deposit today

$33534.73

Step-by-step explanation:

Let the lump sum be P.

The interest, I, on a rate, R%, per annum after T years is given by

The amount, A, is

After 2 years at 4.5% interest rate, the amount is

$7500 is added after 2 years. The principal for the beginning of the third year is then

1.09P + 7500

The amount after the next 3 years is

This is the amount expected to be saved.

Solving for P, we have