Math Help???????

Question

Use the formula A=P ( 1+ r/n)^nt  to solve the compound interest problem 

 

Find how long it takes a $1700 investment to earn $500 interest if it is invested at 7% compounded quarterly.

 

$500 interest will be earned in approximately ????? years 

Answer 1

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

Since the question is asking about compound interest, the underlying formula you want to use here is

A = P(1 + r/n)^(nt)

In this scenario we’re plugging in A = 1700 + 500 = 2200, P = 1700, r = 7% = 0.07, n = 4, and then solving for the value of t algebraically

2200 = 1700(1 + 0.07/4) ^ (4t)

1.2941 = (1.0175)^(4t)

ln (1.2941) = 4t * ln(1.0175)

t = ln(1.2941) / 4 * ln(1.0175) = 3.72

meaning that it will earn $500 interest in about 3.72 years

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

You need to rearrange to isolate the variable t.

 

Starting with the formula

A = P (1+r/n)^nt

 

Isolate term with unknown exponent

A/P = (1+r/n)^nt

 

It might be useful to plug the values in, at this step, to simplify the work.

 

(1700+500)/1700 = (1 + .07/4)^4t

1.29412 = (1.0175)^4t

 

Rearrange a little, to simplify, a little more, moving the constant part of the exponent into the parentheses

1.29412 = (1.0175⁴)^t

 

Evaluate the statement in parentheses

1.29412 = (1.07186)^t

 

Take log of both sides to eliminate the exponent.

log 1.29412 = log 1.07186^t

 

Use power property of exponents

log 1.29412 = t * log 1.07186

 

Isolate the variable

t = log 1.29412/log 1.07186

 

Evaluate, then round to appropriate figures.