Question

Question #94cd0

Answer 1

`$1166.40`

Explanation:

Recall that the formula for compound interest is:

`color(blue)(|bar(ul(color(white)(a/a)A=P(1+i)^ncolor(white)(a/a)|)))`

where:
`A=`future value
`P=`principal (starting amount)
`i=`interest rate per compounding period
`n=`number of compounding periods

`1`. Start by substituting your values into the formula. Note that in your case, one compounding period would be equal to one year.

`A=P(1+i)^n`

`A=2000(1+0.08)^2`

`2`. Solve for `A`.

`A=$2332.80`

`3`. Since the money is paid back in two equal annual installments, divide the value of `A` by `2`. This is the amount of money that will be paid each year until the debt is paid off.

`x=A-:2`

`x=$2332.80-:2`

`color(green)(|bar(ul(color(white)(a/a)x=$1166.40color(white)(a/a)|)))`

`:.`, the annual installment is `$1166.40`.