Question

What rate of interest (to the nearest tenth) is necessary for $1700 to grow to $17000 in 17 years if it is compounded quarterly?

Answer 1

Answer:

r=13.8%

Step-by-step explanation:

we know 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  

$t=17\ years\\ P=\ 1,700\\ r=?\\n=4\\A=\ 17,000$  

substitute in the formula above  

$17,000=1,700(1+\frac{r}{4})^{4*17}$  

$17,000=1,700(1+\frac{r}{4})^{68}$  

$10=(1+\frac{r}{4})^{68}$  

Elevate both sides to 1/68

$10^{1/68}=(1+\frac{r}{4})$  

$\frac{r}{4}=10^{1/68}-1$  

$r=0.1378\\r=13.8\%$