Question

Topic : Time value money

Subject : Engineering Economics

Today is January 1st 2020 (Year 0), Dr. Sid decided to purchase a 2009 Ducati Sport 1000 from the film Tron Legacy on January 2024. The price for 2009 Ducati Sport 1000 today is $70,000 (without road-tax). The price is expected to increase by 10% every year by taking into consideration the interest rate or/inflation since it is a collectors’ items.

i. Determine the price of the 2009 Ducati Sport 1000 upon the year of intended purchase in including the road-tax which is 5% of the price with respect to the year of purchase.

ii. Dr. Sid is planning to purchase the motorcycle via installment. He shall be paying a 20% down-payment with respect to the price of January 2024 (excluding road-tax). If Dr. Sid is planning to $60k once by selling his 2007 Subaru Impreza WRX STI on a form of investment at 10% interest rate, how long will it take for him to accumulate the sufficient amount for the down-payment?

iii. Upon paying for the down-payment, Dr. Sid shall proceed to make monthly installment for the remaining value of the motorcycle (continuity from part (i) and (ii)). Determine the amount of the installment for which he needs to pay if the duration of the installment is for 20 months, at 10% interest rate and the bank which provided the loan is targeting at 10% increment from the remaining price of the motorcycle (after the down-payment is made) which is calculated in question (ii).

Answer 1

The price of the product is $70000 today and purchase of that is intended in 2024. The rise in price is 10% per year.
1) FV = Cash Flow * (1+Interest Rate) ^ Duration

70000 * (1.10 ^ 4) = 102487
Final Price = Future Price + Road Tax
102487 * 1.05 = 107611.35

2) Sid wants to pay 20% of 2024 price.
102487 * 0.2 = 20497.40

He has $60000 from selling Subaru.
FV = 60000 + 20497.40
= 80497.40

=NPER(10%,,60000,-80497.4)
= 3.0834 Years

He will need 3.0834 years

3) Sid has taken loan for the remaining amount after paying 20% down payment.
The total amount of purchase is $107611.35 and down payment is $20497.40

Loan Amount = 107611.35 - 20497.40
= 87113.95

It is not clear what is meant by the bank targeting 10% increment.
I could assume that bank is estimating 10% excess on the loan amount.

87113.95 * 1.10 = 92825.35

=PMT(10%/12,20,-95825.35,)
= 5221.52

The EMI amount is $5221.52