Question

Find the interest rate needed for an investment of $10,000 to grow to an amount of $11,000 in 4 years if interest is compounded quarterly. (Round your answer to the nearest hundredth of a percent.) %

Answer 1

Answer:

$2.39\%$  

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  

$t=4\ years\\ P=\ 10,000\\A=\ 11,000\\ r=?\\n=4$  

substitute in the formula above  

$11,000=10,000(1+\frac{r}{4})^{4*4}$  

$1.1=(1+\frac{r}{4})^{16}$  

Elevated both sides to (1/16)

$1.005975=(1+\frac{r}{4})$  

$0.005975=\frac{r}{4}$  

$r=0.005975*4=0.0239$  

Convert to percent

$0.0239*100=2.39\%$