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g A person borrows $3,750 on a bank credit card at a nominal rate of 18% per year, which is actually charged at a rate of 1.5% per month.(a)What is the annual percentage yield (APY) for the card? (Round your answer to one decimal place.)%(b)Assume that the person does not place any additional charges on the card and pays the bank $150 each month to pay off the loan. LetBnbe the balance owed on the card after n months. Find an explicit formula forBn.(c)How many months will be required to pay off the debt? (Round your answer up to the nearest whole number.)months

Respuesta :

TomShelby

Answer:

A)  0.195618171

B) It will clear the balance after 32 months.

Explanation:

We calculate the effective rate considering compounding interest:

[tex]1.015^{12} - 1 = 0.195618171[/tex]

2) we sovle for N using the present value of an annuity

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C  $150.00

time n

rate 0.015

PV $3,750.0000

[tex]150 \times \frac{1-(1+0.015)^{-n} }{0.015} = 3750\\[/tex]

[tex](1+0.015)^{-n}= 1-\frac{3750\times0.015}{150}[/tex]

[tex](1+0.015)^{-n} = 0.625[/tex]

[tex]-n= \frac{log0.625}{log(1+0.015)}[/tex]

n = 31.56799396