College algebra word problem

Question

A = P(1 + rt)

 is used to find the principal amount P deposited, earning r% interest, for t years. Use this to find what principal amount P David invested at a 4% rate for 15 yr if A = 10,000

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that we’re trying to use to solve here is

A = P(1 + rt)

Solving that for P yields

P = A / (1 + rt)

From there then we can plug in the values that we know from the information given in the question

P = 10000 / (1 + 0.04*15)

P = 10000 / 1.6

P = 6250

Meaning that David’s initial investment here was $6,250

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Assuming this is SIMPLE interest (interest rate is based on original principal) and not COMPOUNDING Interest:

10000 = P (1 + 0.04*15)

10000 = P ( 1 + 0.6)

10000 = P (1.6)

10000/1.6 = P

100000/16 = P

50000/8 = P

25000/4 = P

12500/2 = P

6250 = P

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If it is COMPOUNDING interest

10000 = P * (1.04)^15

10000 / (1.05)^15 = P

P=5,473.17