Question

How long will it take for 2,900 to grow to 25,600 at an interest rate of 10.4% if the interest is compounded quarterly?

Answer 1

The time taken if the interest is compounded quarterly will be 21.212 years or about 21 years 3 months.

We have,

Principal = 2900,

Amount = 25,600

And,

Rate of Compounded Interest = 10.4%

According to the question,

Interest is compounded quarterly,

So,

Rate of Compounded Interest = $\frac{10.4}{4}$  = 2.6%

Now,

Using the Compound Interest formula,

i.e.

A = P(1 + $\frac{r}{100})^t$

i.e.

25600 = 2900(1 +  $\frac{2.6}{100})^t$

On solving we get,

$\frac{256}{29}$ = ( $\frac{102.6}{100})^t$

On solving further,

t = $\frac{ln(\frac{256}{29}) }{ln(\frac{102.6}{100} )}$

On solving for log,

We get,

t = 21.212 years or about 21 years 3 months

Hence, we can say that the time taken if the interest is compounded quarterly will be 21.212 years or about 21 years 3 months.

Learn more about Compound Interest click here:

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