Question

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

Answer 1

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:

$PV(1+r)^n=FV$

We use logarithmics properties and solve:

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

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