Solve for the unknown number of years in each of the following (Enter rounded answers as directed, but do not use rounded numbers in intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16)):

Present Value Years Interest Rate Future Value
$ 800 10 % $ 1,655
2,491 8 4,250
33,905 13 392,620
33,600 20 214,844

Respuesta :

Answer:

a)   7.627144987

b)   5.605222315

c)  20.04031392

d)  10.17644951

Explanation:

We need to solve for years starting from the future value of a lump sum formula:

[tex]PV(1+r)^n=FV\\[/tex]

We use logarithmics properties and solve:

[tex](1+r)^n=FV/PV\\\\log_{1+r}(FV/PV) = n\\\\n = \frac{log FV/PV}{log (1+r)}[/tex]

a)

log(1655/800)/log1.1 = n

7.627144987

b)

log(4250/2491)/log1.08 = n

5.605222315

c)

log(392620/33905)/log1.13 = n

20.04031392

d)

log(214844/33600)/log1.20 = n

10.17644951