Question

Kaitlyn needs $7148 for a future project. She can invest 4000 now at an annual rate of 9.4%, compounded quarterly. Assuming that no withdrawals are made, how long will it take her to have money for her project? Do not round any intermediate computations and round your answer to the nearest hundredth.

Answer 1

Remember that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

P=$ 4,000

A=$7,148

r=9.4%=0.094

n=4

substitute the given values

$7,148=4,000(1+\frac{0.094}{4})^{4t}$$\frac{7,148}{4,000}=(1.0235)^{4t}$

apply log both sides

$\log (\frac{7,148}{4,000})=4t\cdot\log (1.0235)^{}$

t=6.25 years