mcqs Math Simple Interest Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan. 7456

Question: Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(A)  5.25
(B)  8.75
(C)  7
(D)  10.5

Correct Answer 7

Solution And Explanation

Solution

Given,

Principal (P) = $6700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9514

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9514 – $6700 = $2814

Thus, Simple Interest = $2814

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2814}/_{6700 × 6}

= ²⁸¹⁴⁰⁰/₄₀₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2814 (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 = 6% of Principal

= 6% of $6700

= ⁶/₁₀₀ × 6700

= ^{6 × 6700}/₁₀₀

= ⁴⁰²⁰⁰/₁₀₀ = 402

Thus, simple Interest for 1 year = $402

Now,

∵ If the simple Interest is $402, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₂ years

∴ If the simple Interest is $2814, then the time = ¹/₄₀₂ × 2814 years

= ^{1 × 2814}/₄₀₂ years

= ²⁸¹⁴/₄₀₂ = 7 years

Thus, time (T) = 7 years Answer