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Dana just finished paying off the $15,400 loan she took out four years ago. The loan had 6.68% interest, compounded monthly. If Dana paid a total of $18,321.60, how much did she pay in service charges? a. $730.08 b. $366.49 c. $1,028.72 d. $266.76

Respuesta :

Aliwohaish12
First you need to find the monthly payment of the loan by using the formula of the present value of an annuity ordinary which is
Pv=pmt [(1-(1+r/k)^(-kn))÷(r/k)]
Pv the amount of the loan 15400
PMT monthly payment?
R interest rate 0.0668
K compounded monthly 12
N time 4years
Solve the formula for PMT
PMT=pv÷[(1-(1+r/k)^(-kn))÷(r/k)]
PMT=15,400÷((1−(1+0.0668÷12)^(
−12×4))÷(0.0668÷12))
=366.49

After that find the total amount paid
366.49×12months×4years
=17,591.52

So Service charge is
18,321.60−17,591.52=730.08

Hope it helps!

If Dana paid a total of $18,321.60, the amount that she paid for in service charges is; $730.08

What is the Service Charge?

Using the formula for the present value of an annuity, the monthly payment of the loan is gotten from;

Pv = PMT[(1 - (1 + (r/k))^(-kn)) ÷ (r/k)]

Where;

Pv is the amount of the loan = $15400

PMT is monthly payment

R is interest rate = 6.68% = 0.0668

K is the number of times compounded monthly = 12

N is the time = 4years

Making PMT the subject of the formula gives;

PMT = Pv ÷ [(1 - (1 + (r/k))^(-kn)) ÷ (r/k)]

PMT = 15,400 ÷ ((1 − (1 + 0.0668 ÷ 12)^(−12 × 4)) ÷ (0.0668 ÷ 12))

PMT = 366.49

Thus, the total amount paid is;

A = 366.49 × 12months × 4years

A = $17,591.52

Thus, Service charge is

S.C = 18,321.60 − 17,591.52

S.C = $730.08

Read more about Present Value at; https://brainly.com/question/25792915

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