Respuesta :
Answer:
The capital will first exceed RM 10 000 after 12 complete years.
Step-by-step explanation:
This is a compound interest problem.
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.
In this exercise, we have:
So, for our problem, we have:
We first want to find t, when [tex]A = 10,000[/tex], given that [tex]P = 5,000, n = 1[/tex] and [tex]r = 0.06[/tex].
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]10,000 = 5,000(1 + \frac{0.06}{1})^{t}[/tex]
[tex]1.06^{t} = 2[/tex]
Now we apply log to both sides. Important to remember the following proprierty:
[tex]\log{a^{b}} = b\log{a}[/tex]
[tex]\log{1.06^{t}} = \log{2}[/tex]
[tex]t\log{1.06} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.06}}[/tex]
[tex]t = 11.9[/tex]
11.9 years is 11 years and some 330 days. The next complete year will be the 12th year.
The capital will first exceed RM 10 000 after 12 complete years.
