Question

use the present value formula to determine the amount to be invested​ now, or the present value needed.

The desired accumulated amount is ​$50,000 after 14 years invested in an account with ​7% interest compounded annually


The amount to be invested​ now, or the present value​ needed, is ​???


​(Round to the nearest cent as​ needed.)

Answer 1

The amount to be invested​ now, or the present value​ needed, is $22873.75

How to find the present value?

We solve the problem using the compound interest formula for amount

A = P(1 + r)ⁿ where

• P = present value,
• r = interest rate and
• n = number of years.

What is the present value?

Making P subject of the formula, we have

P = A/(1 + r)ⁿ

Given that

• A = $50,000,
• r = 7% = 0.07 and
• n = 14

Substituting the values of the variables into the equation, we have

P = A/(1 + r)ⁿ

P = 50000/(1 + 0.07)¹⁴

P = 50000/(1.07)¹⁴

P = 50000/1.7317

P = 22873.75

So, the amount to be invested​ now, or the present value​ needed, is $22873.75

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