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

r=13.8%

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(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+(r)/(4))^(4*17)`

`17,000=1,700(1+(r)/(4))^(68)`

`10=(1+(r)/(4))^(68)`

Elevate both sides to 1/68

`10^(1/68)=(1+(r)/(4))`

`(r)/(4)=10^(1/68)-1`

`r=0.1378\\r=13.8\%`