mcqs Math Simple Interest Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan. 8031

Question: Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 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) = $5300

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

Amount (A) = $10600

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10600 – $5300 = $5300

Thus, Simple Interest = $5300

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5300}/_{5300 × 10}

= ⁵³⁰⁰⁰⁰/₅₃₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5300

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

Simple Interest = $5300 (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 $5300

= ¹⁰/₁₀₀ × 5300

= ^{10 × 5300}/₁₀₀

= ⁵³⁰⁰⁰/₁₀₀ = 530

Thus, simple Interest for 1 year = $530

Now,

∵ If the simple Interest is $530, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₀ years

∴ If the simple Interest is $5300, then the time = ¹/₅₃₀ × 5300 years

= ^{1 × 5300}/₅₃₀ years

= ⁵³⁰⁰/₅₃₀ = 10 years

Thus, time (T) = 10 years Answer