A sum of money becomes two times of itself in 8 years at simple interest, and it becomes four times of itself in 2 years at compound interest, when interest is compounded annually. Find the ratio of the rate of simple interest to the rate of compound interest offered per year.
Answer & explanation
Correct answer: option 4
A sum of money becomes two times of itself in 8 years at simple interest
Simple interest = \(\frac{P × R × T}{100}\)
P + \(\frac{P × R × 8}{100}\) = 2P
\(\frac{1 × R × 8}{100}\) = 1
R = 12.5%
A sum of money becomes four times of itself in 2 years at compound interest
4P = P [ 1 + \(\frac{R}{100}\) ]²
2 = [ 1 + \(\frac{R}{100}\) ]
\(\frac{R}{100}\) = 1
R = 100%
Now,
Ratio of rate of simple interest to compound interest
12.5 : 100
1 : 8