You want to buy a new sports car from Roy's Cars for $51,800. The contract is in the form of a 48-month annuity due at an APR of 7.8 percent, compounded monthly. What would be your monthly payment?A) $1,251.60B) $1,109.29C) $1,245.70D) $1,152.98E) $1,084.32

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valetta valetta · Answer 1 · 2019-11-08T10:33:49+01:00

Answer:

option (A) $1251.60

Explanation:

Data provided in the question;

Cost of the Roy's Cars = $51,800

Duration of the annuity = 48 months

Interest rate = 7.8%

Monthly interest rate, i = [tex]\frac{7.8\%}{12}[/tex] = 0.65% = 0.0065

Now,

Present value of annuity is given using the formula

Present value = PMT × [tex][\frac{1}{i}-\frac{1}{i(1+i)^n}][/tex] × (1 + i)

on substituting the respective values, we get

$51,800 = PMT × [tex][\frac{1}{0.0065}-\frac{1}{0.0065(1+0.0065)^{48}}][/tex] × (1 + 0.0065)

or

$51,800 = PMT × [153.84 - 112.72 ] × (1.0065)

or

$51,800 = PMT × 41.387

or

PMT = $1251.60

Hence,

the monthly payment will be option (A) $1251.60