# 2010-08-11_024345_p4-3 by ajizai

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```									P4–3 Future value tables. Use the future value interest factors in Appendix Table A–1 in each of the
cases shown in the table on the facing page to estimate, to the nearest year, how long it would take an
initial deposit, assuming no withdrawals, a. To double. b. To quadruple.

Case            Interest Rate
A               7%
B               40%
C               20%
D               10%

Case A
a.      2         =   1 x (1 + .07)n    b.      4         =   1 x (1 + .07)n

2         =   (1.07)n                   4         =   (1.07)n

Log(2) =      n x Log(1.07)             Log(4) =      n x Log(1.07)

n= Log(2)/Log(1.07) = 10.24             n= Log(4)/Log(1.07) = 20.49

10 years                                20 years

Case B
a.      2         =   1 x (1 + .40)n    b.      4         =   1 x (1 + .40)n

2         =   (1.40)n                   4         =   (1.40)n

Log(2) =      n x Log(1.40)             Log(4) =      n x Log(1.40)

n= Log(2)/Log(1.40) = 2.06              n= Log(4)/Log(1.40) = 4.12

2 years                                 4 years

Case C
a.      2         =   1 x (1 + .20)n    b.      4         =   (1 + .20)n

2         =   (1.20)n                   4         =   (1.20)n

Log(2) =      n x Log(1.20)             Log(4) =      n x Log(1.20)

n= Log(2)/Log(1.20) = 3.80              n= Log(4)/Log(1.20) = 7.60

4 years                                 8 years
Case D
a.   2         =   1 x (1 +.10)n   b.   4      =   (1 +.10)n

2         =   (1.10)n              4      =   (1.10)n

Log(2) =      n x Log(1.10)        Log(4) =   n x Log(1.10)

n= Log(2)/Log(1.10) = 7.27         n= Log(4)/Log(1.10) = 14.54

7 years                            15 years

```
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