Question

Diane Wallace bought a​ living-room suite on​ credit, signing an installment contract with a finance company that requires monthly payments of ​$49.06 for three years. The first payment is made on the date of signing and interest is 20​% compounded monthly. ​(a) What was the cash​ price? ​(b) How much will Diane pay in​ total? ​(c) How much of what she pays will be​ interest? ​(d) Based on the cash price calculated in part​ (a), if the interest rate is changed to 17.7​% compounded​ monthly, what is the new monthly​ payment?

Answer 1

a) The cash price is equal to the principal amount in the given question. We can find the principal amount or cash price by the compound interest formula

Compound Interest =

A = P ( 1 + r )^t

^{Here A is the total amount that include cash price plus interest A = $49.06 × 36 = $ 1766.16}    r (rate)= 0.2 or 20% t (time in years) = 3 years

Now, on applying these values in the above formula =

P = A / (1+r) ^t = $ 974.09

Thus the cash price = $974.09

(b) The total amount paid by Daine is = $49.06 × 36

= $1766.16 .

As we have seen in the question that $49.06 is being paid every month for 3 years, the total amount paid by her would be $1766.16 .

( C) To calculate the interest paid by her =

Interest = Amount - Principal ( Cash Price )

= $1766.16 - $974.09

= $ 792.07

(d)The new monthly intallment to be paid if on the same cash price interest would be 17.7% compounded monthly would be =

P = $974.09

r = 17.7%

t = 3 years

A = P (1+ r) ^t

A = $ 1650.16 (by applyig the values in the formula)

Now , the total amount calculated is $ 1650.16 which is to be paid in 3 years (36 months) as equal monthly installment.

So, to know the monthly payment , we dill divide this amount by 36 . = $1650.16 / 36 = $ 45.84

So, the new monthly payment = $ 45.84

^​