Question

A man invested rupees 16000 at a simple interest rate of 8% per annum for 2 years. had he invested the sum at a compound interest rate of 8% per annum for the same period, how much more would have been earned?
A. Rs. 102.40
B. Rs. 201.85
C. Rs. 100
D. Rs. 95.81

Answer 1

Hint- To solve this question, we need to use the basic formulas of simple interest and compound interest.
Simple Interest (SI) = $\dfrac{{{{P \times T \times R}}}}{{{\text{100}}}}$
Compound Interest(C.I.)= P${\left( {{\text{1 + }}\dfrac{{\text{r}}}{{\text{n}}}} \right)^{{\text{nt}}}}$−P
Where,
C.I.$ \to $Compound Interest
P $ \to $ Principal Amount
A $ \to $ Total Accumulated Amount
r $ \to $ Rate of Interest
n $ \to $ Compounding Frequency Per Annum
t $ \to $ Time (in Years)

Complete step-by-step answer:
Now, using above formula-
Simple Interest (SI) = $\dfrac{{{{P \times T \times R}}}}{{{\text{100}}}}$
                                   = $\dfrac{{16000 \times 2 \times 8}}{{100}}$
                                   = 2560 Rs.
Compound Interest= P${\left( {{\text{1 + }}\dfrac{{\text{r}}}{{\text{n}}}} \right)^{{\text{nt}}}}$−P
= 16000${\left( {1 + \dfrac{8}{{100}}} \right)^2}$- 16000
=16000${\left( {\dfrac{{27}}{{25}}} \right)^2}$- 16000
= 18662.40 – 16000
= 2662.40 Rs.
Diff of interest= (2662.40-2560)Rs.=102.40 Rs.
Therefore, option (A) is the correct answer.

Note- After the calculation for S.I. is done, the principal has to be added to it to get the total amount that the borrower has to give or the lender will collect. This is called total amount and its formula is given as A = P + S.I.