Simple interest question with explanation solved answer

Question:

 A sum of Rs. 1600 gives a simple interest of Rs. 252 in 2 year and 3 months.
The rate of interest per annum is :

1. 5%
2. 7%
3. 8%
4. 6%

Answer:
Simple Interest Equation (Principal + Interest)
A = P(1 + rt)

Where:

A = Total Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
r = Rate of Interest per year in decimal; r = R/100
R = Rate of Interest per year as a percent; R = r * 100
t = Time Period involved in months or years
From the base formula, A = P(1 + rt) derived from A = P + I and I = Prt so A = P + I = P + Prt = P(1 + rt)

Note that rate r and time t should be in the same time units such as months or years.

Equation:
r = (1/t)(A/P - 1)

Calculation:
Solving our equation:
r = (1/27)((1852/1600) - 1) = 0.00583333
r = 0.00583333

Converting r decimal to R a percentage
R = 0.00583333 * 100 = 0.5833%/month

Calculating the annual rate
0.5833%/month × 12 months/year = 6.9996%/year.
The interest rate required to get a total amount, principal plus interest, of $1,852.00 from simple interest on a principal of $1,600.00 over 2.25 years (27 months) is 0.5833% per month and in year is 7%.
i.e. option 2. 7% is the right answer.