Bill O\'Brien would like to take his wife, Mary, on a trip four years from now t
ID: 2417752 • Letter: B
Question
Bill O'Brien would like to take his wife, Mary, on a trip four years from now to Europe to celebrate their 40th anniversary. He has just received a $19000 inheritance from an uncle and intends to invest it for the trip. Bill estimates the trip will cost $23700 and he believes he can earn 5% interest, compounded annually, on his investment. What amount will he have after four years? Assume that the trip will cost $25300. What interest rate, compounded annually, must Bill earn to accumulate enough to pay for the trip? Bill's total in 4 years Interest rate needed to meet new cost (in %) | Don James purchased a new automobile for $24000. Don made a cash down payment of $6000 and agreed to pay the remaining balance in 48 monthly installments, beginning one month from the date of purchase. Financing is available at a 12% annual interest rate. Calculate the amount of the required monthly payment. Payment amounts Determine the combined present value as of December 31, 2013, of the following four payments to be received at the end of each of the designated years, assuming an annual interest rate of 4%.Explanation / Answer
1) a) Amount Bill will have after four years, is the FV of the investment of $19000 compounded annually at 5%
The future value = 19000*1.05^4 = $23,095.
b) If Bill has to accumulate 25300 by the end of the 4th year, the interest rate can be found out by solving the following equation for 'i' the interest rate,
25300 =19000*(1+i)^4
1.33157895 = (1+i)^4
(1.33157895)^1/5 - 1 = i
1.05894495 - 1 = i
0.05894 = i
i = 5.89%
2) Since Don James is paying $6000 immediately, the loan amount would be 24000 - 6000 = $18000
This loan is to be rapaid in 48 monthly instalments, the interest rate being 12% pa (monthly 1%)
The loan amount of 18000 is the PV of the annuity being the monthly payments to be made, the discount rate being 1% per month.
So, 18000 = A*PVIFA(1,48)
18000/PVIFA(1,48) = A
18000/37.974 = $474.
3) The combined PV = 4100/1.04^1 + 5300/1.04^2 + 7300/1.04^4 + 9900/1.04^6
3942.31 + 4900.15 + 6240.07 + 7824.11 = $22,906.64.
4) Since 89000 is to be paid after 2 years and interest rate is 8%, the value to be accounted as sale and note receivable is the PV at 8%
= 89000/1.08^2 = $76,303
5)
a) PV of cost for Machine A = 49000 + 1400*PVIFA(6,10) - 5000*PVIF(6,10)
49000+1400*7.3601-5000*1.7908 = 49000+10304.14-8954 = $68,258
b) PV of Machine B = 45000 + 4000/1.06^3 + 5000/1.06^6 + 5000/1.06^8
=45000 + 3358.48 + 3524.80 + 3137.06 = 55020.34 =$55,020
6) Esquire should prefer Machine B, as the PV of the cash outflows associated with it is lower; both the machines having the same life of 10 years.
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