I need help with a math word problem?

Question

here it is:

an owner's share of a business is $32,500. The business has grown at a rate of 7% APR compounded quarterly for the last 5 years 3 months. What was the owner's share worth 5 years 3 months ago?

it gives the equation [ A = P (1 + r/n ) ^nt ]

can anyone show me how to do this? I'd really appreciate it.

Answer 1

compound quarterly means n = 4 (4 times per year).

A = amount plus the interest
P = amount originally invested
r = interest rate
t = time in years

In this case, t = 5.25

So...
32500 = P(1 + 0.07/4]^(4*5.25)
32500 = P(1.0175)^(21)
32500 = P(1.439536814)
22576.7064 = P
$22,576.71 = P

Answer 2

P is the owner's share right now, so that is $32,500

r is the rate (APR), so that is 7%, which is.07

n is the number of times a year the rate is done, so that is done quarterly, which is 4 times a year

t is the number of years invested, which is 5... but it is 5 years and 3 months. so this becomes 5.25 (n is 4 times a year, so every 3 months the rate is done... so 3 months is 1/4 of a year, 1/4 = .25)


so the equation becomes
A = 32,500 * (1 + .07/4)^4*5.25\
= $46,784.95

Answer 3

Compounded quarterly means every three months. Your 5 years and three months is 21 periods of time.

So 32500 / (1 - 0.07/4)^(21) = $22576.71

Answer 4

32500 = P (1+ .07/4)^(4*5.25)
32000 = P(1.0175)^21
P= 32000/(1.0175)^21
P = $22229.37