Question

Betty's Bank offers you a $20,000, seven-year term loan at 11 percentannual interest. What will your annual loan payment be?

Answer 1

$4242.86

Step-by-step explanation

to find the annual loan payment we need to use the formula

`A=P(r(1+r)^n)/((1+r)^n-1)`

where

`\begin{gathered} A\text{ is the payment amount per period} \\ P\text{ is the initial principal} \\ r\text{ is the interest rate per period\lparen in decimal\rparen} \\ n=total\text{ number of paymentos of periods} \end{gathered}`

so

Step 1

a)Let

`\begin{gathered} P=20000 \\ r=11\text{ \%=}(11)/(100)=0.11 \\ t=7 \end{gathered}`

b)now, replace to find A

`\begin{gathered} A=P(r(1+r)^n)/((1+r)^n-1) \\ A=20000(0.11(1+0.11)^7)/((1+0.11)^7-1) \\ A=20000(0.11(1.11)^7)/((1.11)^7-1) \\ A=20000(0.2283)/(1.0761) \\ A=4242.86 \end{gathered}`

therefore, the annual loan payment would be $4242.86

I hope this helps you