5. Biaktea purchased a computer in instalment plan by paying 5612.50 cash down
followed by three equal half-yearly instalments of *8788 each. If the rate of interest
charged was 8% per annum, compounded half-yearly, find the cash price of the
computer. Also, find the total interest charged.
Answers
The total interest charged over the installment plan is $ 1976.5.
Given:
Biaktea purchased a computer in an installment plan by paying $ 5612.50 cash down followed by three equal half-yearly installments of $ 8788 each. If the rate of interest charged was 8% per annum, compounded half-yearly.
To find:
Find the cash price of the computer. Also, find the total interest charged.
Solution:
Let's first find the total amount paid by Biaktea over the installment plan:
Each half-yearly installment of $8788 is paid after 6 months, so the interest is compounded for 6 months each time.
The interest rate per half-year is 8%/2 = 4%.
After paying the down payment of $5612.50, Biaktea has to pay $8788 every half-year, so the total amount paid over the three installments is:
=> $8788 + $8788 + $8788 = $26364
Now calculate the present value of these three payments,
which will give us the cash price of the computer:
=> PV = Payment / (1 + r)ⁿ
=> PV = $8788 / (1 + 0.04)¹ + $8788 / (1 + 0.04)² + $8788 / (1 + 0.04)³
=> PV = $ 8450 + $ 8125 + $ 7812.5
=> PV = $ 24387.5
So the cash price of the computer is $ 24387.5 + $5612.50
= $ 30000
Finally, let's calculate the total interest charged:
Total interest = Total amount paid - Cash price
= $5612.50 + $26364 - $ 30000
= $ 1976.5
Therefore,
The total interest charged over the installment plan is $ 1976.5.
Learn more at
https://brainly.in/question/13821233
#SPJ1
The cash price of the computer is $ 30000 and the total interest charged over the installment plan is $ 1976.5.
Given:
down payment = $ 5612.50
three equal half-yearly installments of $ 8788 each = paid.
To find:
cash price of the computer =?
Solution:
The total sum paid by Biaktea during the payment plan:
The interest is compounded for 6 months for each of the six months between each half-yearly payment of $8788.
8%/2 = 4% is the interest rate for a half-year.
Biaktea must pay $8788 every six months after making a down payment of $5612.50, making the total sum paid throughout the three payments:
= $8788 + $8788 + $8788 = $26364
We can now determine the cash cost of the computer by calculating the present value of these three payments:
= PV = Payment / (1 + r)ⁿ
= PV = $8788 / (1 + 0.04)¹ + $8788 / (1 + 0.04)² + $8788 / (1 + 0.04)³
= PV = $ 8450 + $ 8125 + $ 7812.5
= PV = $ 24387.5
Hence, the cash price of the computer is $ 24387.5 + $5612.50 = $ 30000
The total interest charged:
Total interest = Total amount paid - Cash price
= $5612.50 + $26364 - $ 30000
= $ 1976.5
Therefore, the total interest charged during the installment plan is $ 1976.5.
∴ The cash price of the computer is $ 30000 and the total interest charged during the installment plan is $ 1976.5.
#SPJ1