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

`2.39\%`

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

substitute in the formula above

`11,000=10,000(1+(r)/(4))^(4*4)`

`1.1=(1+(r)/(4))^(16)`

Elevated both sides to (1/16)

`1.005975=(1+(r)/(4))`

`0.005975=(r)/(4)`

`r=0.005975*4=0.0239`

Convert to percent

`0.0239*100=2.39\%`