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 $10070 to clear the loan, then find the time period of the loan. 7876

Question: Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan.

(A)  6.75
(B)  11.25
(C)  9
(D)  13.5

Correct Answer 9

Solution And Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $10070

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10070 – $5300 = $4770

Thus, Simple Interest = $4770

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4770}/_{5300 × 10}

= ⁴⁷⁷⁰⁰⁰/₅₃₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5300

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

Simple Interest = $4770 (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 $4770, then the time = ¹/₅₃₀ × 4770 years

= ^{1 × 4770}/₅₃₀ years

= ⁴⁷⁷⁰/₅₃₀ = 9 years

Thus, time (T) = 9 years Answer