You have decided to buy a used car. The dealer has offered you two options: (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use the appropriate factor(s) from the tables provided.)
a. Pay $500 per month for 20 months and an additional $10,000 at the end of 20 months. The dealer is charging 24 percent per annum.
b. When you buy the car, pay cash equal to the present value of the payments in option (a).
Determine how much cash the dealer would charge in option (b).

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sharry187 sharry187 · Answer 1 · 2019-11-07T07:27:44+01:00

Answer:

$21,635.14

Explanation:

In order to calculate present value of the annuity and future value, following formula will be used:

[tex]PV=PMT(1+(1/(1+r)^n)/r+FV/(1+r)^n[/tex]

PV = Present Value

PMT = Annuity Payment

r = Interest Rate

FV = Future Value

n = Number of periods

Since the payment is monthly, the interest rate will also be calculated on a monthly basis:

Interest rate = 24%/12 = 2% per month

Solution:

500 (1+(1/(1+0.02)^20)/0.02 + 20000/(1+0.02)^20 = 21,635.14

Or

A finance calculator can also be used to calculate the present value

Following instructions needs to be inserted

I/Y = 2%

n = 20

PMT = 500

FV = 20,000

Press CPT then PV

Parrain Parrain · Answer 2 · 2022-04-05T14:32:08+02:00

Based on the amount paid per month, and the period of payment, the amount in cash you will pay for the used car is $14,905.41.

Monthly interest:

= 24% / 12

= 2%

Present value can be found as:

= (Payments x Present value interest factor of annuity, 20 periods, 2%) + (Additional amount x Present value factor, 2%, 20 periods)

= (500 x 16.3514) + (10,000 x 0.6729713)

= $14,905.413

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