Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)):
Present Value | Years | Interest Rate | Future Value | |||||||
$ | 510 | 9 | % | $ | 1,212 | |||||
760 | 10 | 1,629 | ||||||||
17,900 | 17 | 260,563 | ||||||||
21,000 | 15 | 391,887 | ||||||||
|
Explanation:
We
can use either the FV or the PV formula. Both will give the same answer
since they are the inverse of each other. We will use the FV formula,
that is:
|
FV = PV(1 + r)t |
Solving for t, we get: |
t = ln(FV / PV) / ln(1 + r) |
FV = $1,212 = $510(1.09)t; | t = ln($1,212/ $510) / ln(1.09) | = | 10.04 years | |
FV = $1,629 = $760(1.10)t; | t = ln($1,629/ $760) / ln(1.10) | = | 8.00 years | |
FV = $260,563 = $17,900(1.17)t; | t = ln($260,563 / $17,900) / ln(1.17) | = | 17.06 years | |
FV = $391,887 = $21,000(1.15)t; | t = ln($391,887 / $21,000) / ln(1.15) | = | 20.94 years | |
Calculator Solution: |
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. |
Enter | |
9%
|
$510
| |
±$1,212
| ||||||||||
| |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
Solve for |
10.04
| | | | |
Enter | |
10%
|
$760
| |
±$1,629
| ||||||||||
| |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
Solve for |
8.00
| | | | |
Enter | |
17%
|
$17,900
| |
±$260,563
| ||||||||||
| |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
Solve for |
17.06
| | | | |
Enter | |
15%
|
$21,000
| |
±$391,887
| ||||||||||
| |
N
| | |
I/Y
| | |
PV
| | |
PMT
| | |
FV
| |
Solve for |
20.94
| | | | |
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