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1)If interest is 7% compounded annually, calculate the future value of four year cash flows of $10,000 in year 1; $20,000 in year 2; $30,000 in year 3 and $40,000 in year 4
1)If interest is 7% compounded annually, calculate the future value of four year cash flows of $10,000 in year 1; $20,000 in year 2; $30,000 in year 3 and $40,000 in year 4. Multiple Choice $105,248.43 $107.248.43 $109,248.43 $111,248.43 $113,248.43
2)You just bought a new car for $27,718. The car loan contract specifies that the interest rate on your car loan is 4.5% APR compounded monthly, your down-payment is $2,718, and the term for the loan is 5 years. You must make monthly payments on your loan starting in one month's time. What is the monthly payment? Multiple Choice $5,694.79 $474.57 $466.08 $416.67 ? O $516.75
Expert Solution
1)
| 7% | |||
| Year | Total cash flow | Future value factor(1+r)^(4-T) | Future values |
| 1 | $ 10,000 | 1.225 | $ 12,250.43 |
| 2 | $ 20,000 | 1.145 | $ 22,898.00 |
| 3 | $ 30,000 | 1.070 | $ 32,100.00 |
| 4 | $ 40,000 | 1.000 | $ 40,000.00 |
| Total | $107,248.43 | ||
| Option 2 is the right answer. |
2)
The car price is $ 27718 and down payment is $ 2718.
Amount of Loan being remaining amount due = 27718-2718
=$ 25000
Interest Rate is 4.5 APR compounded monthly and loan period is 5 years
Monthly Payment = Loan Amount / PVAF(r%,n period)
PVAF(r%,n period) is Present Value annuity factor where r% is rate of interest which is to be converted to monthly rate and n period is no. of months i.e 60 months.
PVAF(0.375%, 60 months)= (1+r%)n-1/ (r% *(1+r%)n)
= (1+0.375%)60-1/(0.375% *(1+0.375%)60)
= (1.00375)60-1/ (0.00375 *(1.00375)60)
= 1.251795821 - 1/ (0.00375*1.251795821)
=0.251795821/ 0.00469423
= 53.6394
Therefore:
Monthly Amount = 25000/53.6394
= $ 466.08
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