Question

Please Help! Algebra 2!

Answer 1

The interest rate of the account is
`3\%`

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=14\ years\\ P=\$1,863\\ A=\$2,830.97\\n=4`

substitute in the formula above and solve for r

`\$2,830.97=\$1,863(1+(r)/(4))^(4*14)`

`(2,830.97/1,863)=(1+(r)/(4))^(56)`

`(2,830.97/1,863)^(1/56)=(1+(r)/(4))`

`[(2,830.97/1,863)^(1/56)-1]=(r)/(4)`

`r=4*[(2,830.97/1,863)^(1/56)-1]\\ \\r= 0.03`

Convert to percent

`r= 0.03*100=3\%`