Question

(b) After how many complete years will a starting capital of RM5 000 first exceed RM10 000 if it grows at 6% per annum?

Answer 1

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:

$A = P(1 + \frac{r}{n})^{nt}$

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 $A = 10,000$, given that $P = 5,000, n = 1$ and $r = 0.06$.

$A = P(1 + \frac{r}{n})^{nt}$

$10,000 = 5,000(1 + \frac{0.06}{1})^{t}$

$1.06^{t} = 2$

Now we apply log to both sides. Important to remember the following proprierty:

$\log{a^{b}} = b\log{a}$

$\log{1.06^{t}} = \log{2}$

$t\log{1.06} = \log{2}$

$t = \frac{\log{2}}{\log{1.06}}$

$t = 11.9$

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.