After 5 years, Ingrid still owes approximately $1463.15. Since she wants to pay it off three years early, this is the amount she needs to pay to clear the loan.
To determine Ingrid's payoff quote, we'll first find out how much she still owes on the loan after 5 years (8 years - 3 years paid off early).
We'll use the formula for the remaining balance on a loan:
A=P×(1− 1/(1+r)^n )/r
Where:
A is the remaining balance on the loan.
P is the initial loan amount ($12830).
r is the monthly interest rate, which can be found by dividing the annual percentage rate (APR) by 12 months and converting it to a decimal.
n is the total number of payments over the loan period.
First, convert the APR to a monthly interest rate:
r= 3.7%/ 12×100 =0.0030833
Now, calculate the remaining balance after 5 years:
n=8×12 months−5×12 months=36 months
A=12830×(1− (1+0.0030833)^36
A≈12830×(1− (1.0030833)^36
A≈12830×(1− 1.1282981 )/0.0030833
A≈12830×(1−0.886913)/0.0030833
A≈12830×0.113087/0.0030833
A≈1463.15
So, after 5 years, Ingrid still owes approximately $1463.15. Since she wants to pay it off three years early, this is the amount she needs to pay to clear the loan.