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4. In a previous homework, we learned that skipping your daily Starbucks fix would save you S180 per month. If you invested those savings in a retirement account earning 0.25% per month compound interest, you would have an additional S166,691 saved up by time you retire. Assuming you will live 20 years after retiring, how much additional monthly income will this provide you in your retirement?

66 A concept car that will get 100 miles per gallon and carry four persons would have a carbon-fiber and aluminum composite frame with a 900 cc three-cylinder turbodiesel/electric hybrid power plant. The extra cost of these technologies is esti- mated to be $11,000. (a) If gasoline savings over a comparable conventional car would be $900 in year one, increasing by 10% each year, what is the present worth of the savings over a 10-year period at an interest rate of 8% per year? (b) Compare the present worth values to determine if the extra cost is recovered by fuel savings

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Answer #1

(a) Present worth (PW) of savings is computed as follows. Note that

Saving in year N = savings in year (N - 1) x 1.10

PV Factor in year N = (1.08)-N

Year Savings ($) PV Factor @8% Discounted Savings ($)
(A) (B) (A) x (B)
1 900.00 0.9259 833.33
2 990.00 0.8573 848.77
3 1089.00 0.7938 864.48
4 1197.90 0.7350 880.49
5 1317.69 0.6806 896.80
6 1449.46 0.6302 913.41
7 1594.40 0.5835 930.32
8 1753.85 0.5403 947.55
9 1929.23 0.5002 965.10
10 2122.15 0.4632 982.97
PW of Savings ($) = 9063.21

(b) Since PW of savings is less than the PW of extra cost ($9063.21 < $11000), extra cost is not recovered by savings.

[Screenshot follows:

E 284 PW - Microsoft Excel Home nsert Page Layout Data Review Vie novaP Cut Calibri Wrap Text General E Copy Paste Merge & Center % , ta:: Conditional Format Cell Inser Formatting as Table Styles Clipboard Font Alignment Number Styles C13 f PW of Savings (S)- Savings ($) Discounted Savings ($) (A) x (B) 1 Year PV Factor @8% 1.08)A(-A3) 1.08)A(-A4) 1.08)A(-A5) 900 B3*1.1 -B4*1.1 B5*1.1 B6*1.1 B7*1.1 -B8*1.1 B9*1.1 B10*1.1 B11*1.1 B3* C3 B4*C4 B5*C5 B6*C6 B7* C7 B8* C8 B9*C9 B10*C10 B11*C11 B12* C12 1.08)A(-A7) 10 8 11 9 12 10 13 14 15 16 1.08)A(-A9) 1.08)A(-A10) 1.08)A(-A11) 1.08)A(-A12) PW of Savings (S) SUM(D3:D12) H Sheet1 Sheet2 Sheet3 Ready

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