Mathematics: 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.) %

I hope this helps you Step-by-step explanation:...

Find the interest rate needed for an investment

ebonsell4910

09.03.2022

$2.39\%$

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

$0.0239*100=2.39\%$

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