Question

Question #cf901

Answer 1

`50.67796` years

Explanation:

An investment of `I` at an annual (compound) rate of `r` for a period of `n` years yields
`color(white)("XXX")v=I*(1+r)^n`

We are told
`color(white)("XXX")v=2467174` (forints)
`color(white)("XXX")r=7%=0.07` and
`color(white)("XXX")I=80000` (forints)

Therefore
`color(white)("XXX")80000 * (1.07)^n=2467174`
or
`color(white)("XXX")(1.07)^n=2467174/80000`

Taking the `log_(1.07)` of both sides (use a calculator)
`color(white)("XXX")n=log_1.07 (2467174/80000)=50.67796`