## 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

Question

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

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2021-10-18T14:47:18+00:00
2021-10-18T14:47:18+00:00 1 Answer
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## Answers ( )

Answer:

$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