mcqs Math Simple Interest Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan. 7907

Question: Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8480 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) = 6% per annum

Amount (A) = $8480

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8480 – $5300 = $3180

Thus, Simple Interest = $3180

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3180}/_{5300 × 6}

= ³¹⁸⁰⁰⁰/₃₁₈₀₀

= 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) = 6% per annum

Simple Interest = $3180 (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 $5300

= ⁶/₁₀₀ × 5300

= ^{6 × 5300}/₁₀₀

= ³¹⁸⁰⁰/₁₀₀ = 318

Thus, simple Interest for 1 year = $318

Now,

∵ If the simple Interest is $318, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₁₈ years

∴ If the simple Interest is $3180, then the time = ¹/₃₁₈ × 3180 years

= ^{1 × 3180}/₃₁₈ years

= ³¹⁸⁰/₃₁₈ = 10 years

Thus, time (T) = 10 years Answer