Question

In: Finance

You are a college student and you plan to purchase a new car after you graduate...

You are a college student and you plan to purchase a new car after you graduate and begin your first job. You want to start saving for a down payment now on a new car in the future . You decide to make monthly payment into a saving account, which earns 2.5% annual interest compounded monthly. You will calculate a monthly payment into the saving account for each scenario.

A.To save $4,000 for 3 years.

B.To save $5,000 for 3 years.

C.To save $5,000 for 4 years.

Expert Solution

Formula for future value of annuity can be used to compute periodic payment as:

FV = P x [(1+r) ⁿ – 1/r]

P = FV/ [(1+r) ⁿ – 1/r]

FV= Future Value

P = Periodic cash flow

r = Rate per period = 2.5 % p.a. or 0.025/12 = 0.00208333333 p.m.

n = Numbers of periods

A.

FV = $ 4,000; n = 3 x 12 = 36 periods

P = $ 4,000/ [(1+0.00208333333)³⁶ – 1/0.00208333333]

= $ 4,000/ [(1.00208333333)³⁶ – 1/0.00208333333]

= $ 4,000/ [(1.07780006111199 – 1)/0.00208333333]

= $ 4,000/ (0.07780006111199/0.00208333333)

= $ 4,000/ 37.2663910788834

= $ 107.1121693337 or $ 107.11

Required monthly payment is $ 107.11

B.

FV = $ 5,000; n = 3 x 12 = 36 periods

P = $ 5,000/ [(1+0.00208333333)³⁶ – 1/0.00208333333]

= $ 5,000/ [(1.00208333333)³⁶ – 1/0.00208333333]

= $ 5,000/ [(1.07780006111199 – 1)/0.00208333333]

= $ 5,000/ (0.07780006111199/0.00208333333)

= $ 5,000/ 37.2663910788834

= $ 133.8902116671 or $ 133.89

Required monthly payment is $ 133.89

C.

FV = $ 5,000; n = 4 x 12 = 48 periods

P = $ 5,000/ [(1+0.00208333333)⁴⁸ – 1/0.00208333333]

= $ 5,000/ [(1.00208333333)⁴⁸ – 1/0.00208333333]

= $ 5,000/ [(1.10505596154990– 1)/0.00208333333]

= $ 5,000/ (0.10505596154990/0.00208333333)

= $ 5,000/ 50.426861624635

= $ 99.153503488255 or $ 99.15

Required monthly payment is $ 99.15

jeff jeffy answered 1 year ago

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