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# Math Help???????

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

### 1 Answer by Expert Tutors

Regina G. | Biotech Grad with Homeschool Experience, Math and Science FocusBiotech Grad with Homeschool Experience,...
5.0 5.0 (279 lesson ratings) (279)
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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 1.07186t

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.