mcqs Math Simple Interest Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan. 8014

Question: Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 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) = 9% per annum

Amount (A) = $12730

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $12730 – $6700 = $6030

Thus, Simple Interest = $6030

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 6030}/_{6700 × 9}

= ⁶⁰³⁰⁰⁰/₆₀₃₀₀

= 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) = 9% per annum

Simple Interest = $6030 (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 = 9% of Principal

= 9% of $6700

= ⁹/₁₀₀ × 6700

= ^{9 × 6700}/₁₀₀

= ⁶⁰³⁰⁰/₁₀₀ = 603

Thus, simple Interest for 1 year = $603

Now,

∵ If the simple Interest is $603, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₃ years

∴ If the simple Interest is $6030, then the time = ¹/₆₀₃ × 6030 years

= ^{1 × 6030}/₆₀₃ years

= ⁶⁰³⁰/₆₀₃ = 10 years

Thus, time (T) = 10 years Answer