Question

11. At what rate per cent per annum will a sum of money
double itself in 5 years if lent at compound interest?

Answer 1

Answer:

At what rate percent will a sum of money double itself in 5 years?

Considering as Simple InterestA=P(1+TR%)

Given that, A=2P for T=5 years and R%=?

⇒2P=P(1+5R%)

2=1+5R%

5R%=1

R%=15

R%=20%

Check: Let principal be 100, A=100(1+5×20%)

A=200

If the interest is compounded.

A=P(1+R%)5

2P=P(1+R%)5

2=(1+R%)5

215=1+R%

1.1487–1=R%

R%=0.1487

R%=14.87%

The rough guess would be using the 72 rule, i.e., divide 72 by either the time or the interest rate to get the one or the other.

In this case, we divide 72 by 5 to get 14.4 as the needed interest rate.

We can check this by:

(1+r)^5=2

Then take the log of each side:

log (1+r)^5=log 2

5 log (1+r)=0.30103

log (1+r)=0.060206

Then:

10^log (1+r)=10^0.060206

1+r=1.148698355

r=14.8698355% √