mcqs Math Simple Interest Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 to clear the loan, then find the time period of the loan. 8000

Question: Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $10070 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) = 9% 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 × 9}

= ⁴⁷⁷⁰⁰⁰/₄₇₇₀₀

= 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) = 9% 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 = 9% of Principal

= 9% of $5300

= ⁹/₁₀₀ × 5300

= ^{9 × 5300}/₁₀₀

= ⁴⁷⁷⁰⁰/₁₀₀ = 477

Thus, simple Interest for 1 year = $477

Now,

∵ If the simple Interest is $477, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₇ years

∴ If the simple Interest is $4770, then the time = ¹/₄₇₇ × 4770 years

= ^{1 × 4770}/₄₇₇ years

= ⁴⁷⁷⁰/₄₇₇ = 10 years

Thus, time (T) = 10 years Answer