Question

The simple interest rate per year that will accumulate the same amount of money in 2 years as a compound interest rate of 20% per year is closest to:

Question 5 options:

	44%
	10%
	22%
	12.4%

Answer 1

Answer: 3^rd option

Let the simple interest rate is S.

Let the principal sum of money is $1,000.

Hence,

Simple interest for 2 years = Principal × rate × years

                                                = 1,000 × S × 2

                                                = 2,000S

Amount in simple interest method = Principal + Simple interest for 2 years

                                                            = 1,000 + 2,000S

Further,

Amount in compound interest method = Principal (1 + rate) ^ years

                                                            = 1,000 (1 + 0.20) ^ 2

                                                            = 1,000 × 1.20^2

                                                            = 1,000 × 1.44

                                                            = 1,440

Therefore as per the condition,

Simple interest for 2 years = Amount in compound interest method

1,000 + 2,000S = 1,440

2,000S = 1,440 – 1,000

2,000S = 440

S = 440 / 2,000

   = 0.22

This is to be multiplied by 100 in order to get it in the percentage form; (0.22 × 100 =) 22%.