mcqs Math Simple Interest Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan. 8045

Question: Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $13400

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $13400 – $6700 = $6700

Thus, Simple Interest = $6700

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 6700}/_{6700 × 10}

= ⁶⁷⁰⁰⁰⁰/₆₇₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6700

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $6700 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 10% of Principal

= 10% of $6700

= ¹⁰/₁₀₀ × 6700

= ^{10 × 6700}/₁₀₀

= ⁶⁷⁰⁰⁰/₁₀₀ = 670

Thus, simple Interest for 1 year = $670

Now,

∵ If the simple Interest is $670, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₇₀ years

∴ If the simple Interest is $6700, then the time = ¹/₆₇₀ × 6700 years

= ^{1 × 6700}/₆₇₀ years

= ⁶⁷⁰⁰/₆₇₀ = 10 years

Thus, time (T) = 10 years Answer