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Karo-lina-s [1.5K]
3 years ago
6

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

Mathematics
1 answer:
maksim [4K]3 years ago
3 0

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.

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