Question

in how many years will a sum of money double at 5% per annum compound interest?? ​

Answer 1

Considering the formula for compound interest, which is F=P⋅(1+r)t, where:

F is the final amount (principal + interest)

P is the principal (initial value)

r is the interest rate (5% in your case)

t is the period of time the interest rate will be applied by (the answer you’re looking for)

So, we just need to work the formula to get to the desired result.

Replacing F with 2P (since in your case the final amount will be double the initial one): 2P=P⋅(1+r)t

Dividing by P on both sides: 2=(1+r)t

Applying log2 on both sides to get t down: log22=log2(1+r)t

Continuing: 1=t⋅log2(1+r)

Isolating t: 1/t=log2(1+r)

Then: t=1/log2(1+r)

When we replace r with 0.05 (5%), we find t=14.2067, which means that applying an interest rate of 5% per year, the initial amount will double in 14.2067 years, or 14 years and almost 2 and a half months (2.48 to be exact).

Answer 2

Answer:

12.5 years

Step-by-step explanation:

To Find:- Number of years to double the amount at 5% per annum.

Solution:-

As we know, Amount after n years when compounded annually becomes

                       $P(1+\frac{r}{100} )^{n}$, where P = Principal, r = rate of interest and

                                                       n =  number of years.

Here we need to double the money so the amount becomes 2P.

∴ $2P = P (1 + \frac{5}{100} )^{n}$

⇒ $2 = (1+\frac{1}{20} )^{n}$

⇒ $ln 2 = n (ln\frac{21}{20} )$

⇒ $n = \frac{ln 2}{ln21-ln20}$

⇒ $n = \frac{0.69}{3.05-2.995}$

⇒ $n = \frac{0.69}{0.055}$

⇒ $n = 12.5$

Therefore, the number of years it will take to double the money at 5% per annum when compounded annually is 12.5 years.

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