Jessica is in the market for a new auto. She has narrowed her hunt down to 2 theoretical accounts. Model A costs \$ 20. 000 and Model B costs \$ 18. 000. With both autos she plans to pay hard currency and have them for 5 old ages before trading in for a new auto. Her research indicates that the trade in value for Model A after 5 old ages is 50 % of the initial purchase monetary value. The trade in value for Model B is 25 % . Jessica has no emotional fond regard to either theoretical account and wants to do a purely fiscal determination. The involvement rate is 6 % . For simpleness assume that operating and care costs for the theoretical accounts are indistinguishable every twelvemonth. Which theoretical account is the better determination and how much “cheaper” is it than the alternate

Model A:
Base Value: 20000
Trade in value after 5 old ages: 50 % = 10000
PV of 10000 = 7472. 58
Model Bacillus:
Base Value: 18000
Trade in value after 5 old ages: 25 % = 4500
PV of 4500 = 3362. 66
Besides. If invested in Model B. Jessica saves 2000. So. PV of investing in Model B is 3362. 66 + 2000 = 5562. 66 So. Jessica additions 2109. 92 if she invests in Model A

Christine is a new homebuyer. She wants to do certain that she incorporates the cost of care into her determination. She estimates that everyday fixs and care on the place she is sing will be \$ 1. 590 in the first twelvemonth ( one twelvemonth from now ) . Due to the increasing age of the place. she expects that care costs will increase 6 % yearly. The involvement rate is 5 % . If she plans to be in the place for 10 old ages. what is the present value of all future care? ( Note that care costs will alter yearly. and starts one twelvemonth from now and she plans to make the last one before selling her house. ) 15000

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14413
15809
19771

Year ============ Cost ============= Present Value
1 ============== \$ 1590 ============ \$ 1590/1. 05
2 ============== \$ 1590 * 1. 06 ======== \$ 1590 * 1. 06 / ( 1. 05 * 1. 05 ) … ============= … =============== …
10 ============= \$ 1590 * power 9 of 1. 06 = \$ 1590 * power 9 of 1. 06/power 10 of 1. 05

Note that
\$ 1590/1. 05 = \$ 1514. 2857
1. 06/1. 05 = 1. 0095238

Adding all footings in the right column. we get the present value of all future care:

\$ 1514. 2857 ( power 10 of 1. 0095238 – 1 ) / ( 1. 0095238 – 1 ) = \$ 15809

1590 is twelvemonth 1. You need to multiply that by 1. 06 to happen twelvemonth 2. and so multiply the reply for that to happen twelvemonth 3 and so on until you get 10 old ages. Merely put it on a spreadsheet should be easy. After you have found each one. so you need to happen the PV for each twelvemonth and add them all up. A spot boring but simple

i= 5 %
n=10
g= 6 %
x= 1590
pv= ?

pv = 1590/1. 05 + 1590 ( 1. 06 ) /1. 05^2 +1590 ( 1. 06 ) ^2/1. 05^3…1590 ( 1. 06 ) ^9/1. 05^10

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