Question

How long does it take $1125 to triple if it is invested at 7% interest, compounded quarterly? round your answer to the nearest tenth?

Answer 1

Answer:

It takes 15.83 years to triple $1125 if it is invested at 7% interest.

Step-by-step explanation:

The future value (FV) of an investment of present value (PV) dollars earning interest at an annual rate of r compounded n times per year for a period of t years is:

$FV=PV(1+\frac{r}{n})^{nt}$

where r/n is the interest per compounding period and nt is the number of compounding periods.

We solve for t,

$PV\left(1+\frac{r}{n}\right)^{nt}=FV\\\\\frac{PV\left(1+\frac{r}{n}\right)^{nt}}{PV}=\frac{FV}{PV}\\\\\left(1+\frac{r}{n}\right)^{nt}=\frac{FV}{PV}\\\\\ln \left(\left(1+\frac{r}{n}\right)^{nt}\right)=\ln \left(\frac{FV}{PV}\right)\\\\nt\ln \left(1+\frac{r}{n}\right)=\ln \left(\frac{FV}{PV}\right)\\\\t=\frac{\ln \left(\frac{FV}{PV}\right)}{n\ln \left(1+\frac{r}{n}\right)}$

When $FV = 3\cdot 1125=3375$, PV = 1125, r = 7%, and n = 4, this becomes

$t=\frac{\ln \left(\frac{3375}{1125}\right)}{4\ln \left(1+\frac{7/100}{4}\right)}\\\\t = \frac{\ln \left(3\right)}{4\ln \left(\frac{407}{400}\right)}\\\\t\approx15.83$

It takes 15.83 years to triple $1125 if it is invested at 7% interest.

Answer 2

To solve this problem you must apply the proccedure shown below:
 1. You have to apply the following formula:
 FV=PV[1+(i/n)]^4t
 FV=3x1125
 FV=3375
 PV=1125
 i=0.07
 n=4
 2. When you substitute the values into the formula, you obtain:
 3375=1125[1+(0.07/4)]^4t
 3. Now, you must solve for t, as following:
 3375/1125=1+(0.07/4)^4t
 3=(1.0175)^4t
 log(3)=log(1.0175)^4t
 log(3)=4t(log(1.0175))
 4t=63.32
 t=15.83 years
 The answer is: 15.83 years.