Question

4. A loan of $14,000 with interest at 12% compounded annually is repaid by payments of $856.00 made at the end of every month. (a) How many payments will be required to amortize the loan? (b) If the loan is repaid in full in 1 year, what is the payout figure? (c) If paid out, what is the total cost of the loan? (a) The number of payments required to amortize the loan is (Round up to the nearest whole number.) (b) The payout figure outstanding principal after the regular payments) is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) (c) The total cost of the loan is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) 5. Four $1000 bonds with 4.4% coupons payable annually are purchased nine months after a coupon matures, to yield 2.2% compounded quarterly. The bonds mature in five years. (a) What is the market price or quoted price of the bonds? (b) What is the accrued interest? (c) What is the cash price? (a) The quoted price of the bonds is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.) (b) The accrued interest is equal to $ (Round to the nearest cent as needed.) (c) The cash price is $ (Round to the nearest cent as needed.)

Answer 1

As per policy, question 4 is being answered, please ask the remaining question 5 seperately.

a) The number of Repayments required.

$856 * Cummulative PV Factor (12% p.a., n months) = $14,000

Cummulative PV Factor (12%/12, n months) = 14000 / 856 = ‭16.35514018691589‬

Hence, n = 18 payments approx.

b) $14000 = $856 * Cummulative PV Factor (12% p.a., 11 months) + Payout Value * PV Factor (12% p.a., 1 Year)

$14000 = $856 * 10.398659 + Payout Value * 0.892857

$14000 = $8901.25 + Payout Value * 0.892857

$14000 - $8901.25 = $5098.75 = Payout Value * 0.892857

Payout Value = $5098.75 / 0.892857 = $5710.60

c) Total Cost of Loan = Total Repayments - Principal Value = Interest

($ 856 * 11) + $5710.60 - $14,000 = $1126.60

Note:- The answer to part c) is based on repayments calculated in part b)

If repayments of part a) are taken, answer would be $856 * 18 - $14000 = $1408 (approx.)

Alternate answers may be possible by making alternate assumptions.

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