We read your photo as:

A car bought in January 2022 for Shs 12,500,000 depreciates at 10% per annum. A brand new car of the same model costs Shs 24,000,000. Calculate: a) The value of the car in January 2025. b) The amount

Mathematics

ScanSolve AI Answer

Answers

4 parts
a

Shs 9,112,500\text{Shs } 9,112,500

b

Shs 22,080,000\text{Shs } 22,080,000

c

Shs 7,320,000\text{Shs } 7,320,000

d

Shs 5,287,500\text{Shs } 5,287,500

Step-by-step solution

9 steps

Here are the solutions to question 2:

Part a· 2 steps

The value of her car in January 2025.

  1. Identify the initial value, depreciation rate, and time period.

    The initial value of the car in January 2022 is Shs 12,500,000\text{Shs } 12,500,000.
    The depreciation rate is 10%10\% per annum.
    The time period from January 2022 to January 2025 is 3 years.

  2. Apply the depreciation formula.

    The formula for depreciation is A=P(1−r)nA = P(1 - r)^n, where AA is the final value, PP is the initial value, rr is the depreciation rate, and nn is the number of years.

    A=12,500,000(1−0.10)3A = 12,500,000(1 - 0.10)^3 A=12,500,000(0.90)3A = 12,500,000(0.90)^3 A=12,500,000×0.729A = 12,500,000 \times 0.729 A=9,112,500A = 9,112,500

    The value of her car in January 2025 is Shs 9,112,500\boxed{\text{Shs } 9,112,500}.

Part b

Shs 22,080,000\text{Shs } 22,080,000

The amount she will pay if she buys the car by paying cash.

  1. Identify the new car price and discount rate.

    The brand new car costs Shs 24,000,000\text{Shs } 24,000,000.
    The cash payment option offers an 8%8\% discount.

  2. Calculate the discount amount.

    Discount=8%×24,000,000\text{Discount} = 8\% \times 24,000,000 Discount=0.08×24,000,000\text{Discount} = 0.08 \times 24,000,000 Discount=1,920,000\text{Discount} = 1,920,000

  3. Calculate the amount to pay after the discount.

    Amount to pay=New car price−Discount\text{Amount to pay} = \text{New car price} - \text{Discount} Amount to pay=24,000,000−1,920,000\text{Amount to pay} = 24,000,000 - 1,920,000 Amount to pay=22,080,000\text{Amount to pay} = 22,080,000

    The amount she will pay if she buys the car by paying cash is Shs 22,080,000\boxed{\text{Shs } 22,080,000}.

Part c

Shs 7,320,000\text{Shs } 7,320,000

The saving she would make if she bought the car by paying cash rather than paying in installments.

  1. Calculate the total cost for the installment option.

    The installment option requires a 60%60\% deposit of the cash value and then Shs 5,000,000\text{Shs } 5,000,000 per month for 3 months.

    Deposit=60%×24,000,000\text{Deposit} = 60\% \times 24,000,000 Deposit=0.60×24,000,000\text{Deposit} = 0.60 \times 24,000,000 Deposit=14,400,000\text{Deposit} = 14,400,000 Total monthly payments=5,000,000×3\text{Total monthly payments} = 5,000,000 \times 3 Total monthly payments=15,000,000\text{Total monthly payments} = 15,000,000 Total installment cost=Deposit+Total monthly payments\text{Total installment cost} = \text{Deposit} + \text{Total monthly payments} Total installment cost=14,400,000+15,000,000\text{Total installment cost} = 14,400,000 + 15,000,000 Total installment cost=29,400,000\text{Total installment cost} = 29,400,000

  2. Calculate the saving.

    The cash payment amount from part b) is Shs 22,080,000\text{Shs } 22,080,000.

    Saving=Total installment cost−Cash payment amount\text{Saving} = \text{Total installment cost} - \text{Cash payment amount} Saving=29,400,000−22,080,000\text{Saving} = 29,400,000 - 22,080,000 Saving=7,320,000\text{Saving} = 7,320,000

    The saving she would make if she bought the car by paying cash rather than paying in installments is Shs 7,320,000\boxed{\text{Shs } 7,320,000}.

Part d

Shs 5,287,500\text{Shs } 5,287,500

How much more money does she need to top on the value of the old car to accomplish the deposit of the new car under the second option of payment.

  1. Identify the value of the old car and the required deposit.

    The value of the old car in January 2025 from part a) is Shs 9,112,500\text{Shs } 9,112,500.
    The deposit for the new car under the second option is Shs 14,400,000\text{Shs } 14,400,000 (calculated in part c).

  2. Calculate the additional money needed.

    Money needed to top up=Required deposit−Value of old car\text{Money needed to top up} = \text{Required deposit} - \text{Value of old car} Money needed to top up=14,400,000−9,112,500\text{Money needed to top up} = 14,400,000 - 9,112,500 Money needed to top up=5,287,500\text{Money needed to top up} = 5,287,500

    She needs to top up Shs 5,287,500\boxed{\text{Shs } 5,287,500} more.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA car costing shs. 800,000 depreciates by 20% in the first year and 5% in the second year…QA motor car costing R200 000 depreciated at a rate of 8% per annum on the reducing balance method…QCalculate the annual rate of depreciation if an item's value depreciates from shs. 800,000 to shs…QDean bought a vehicle for R120 000 at the end of 2008. The value depreciated by 8% p.a. Dean…QA piece of property was purchased on January 1, 2021, for BWP225,000. It is estimated to have a…
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp