mcqs Math Simple Interest Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan. 7973

Question: Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 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) = $5700

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10260

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10260 – $5700 = $4560

Thus, Simple Interest = $4560

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4560}/_{5700 × 8}

= ⁴⁵⁶⁰⁰⁰/₄₅₆₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5700

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4560 (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 = 8% of Principal

= 8% of $5700

= ⁸/₁₀₀ × 5700

= ^{8 × 5700}/₁₀₀

= ⁴⁵⁶⁰⁰/₁₀₀ = 456

Thus, simple Interest for 1 year = $456

Now,

∵ If the simple Interest is $456, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₆ years

∴ If the simple Interest is $4560, then the time = ¹/₄₅₆ × 4560 years

= ^{1 × 4560}/₄₅₆ years

= ⁴⁵⁶⁰/₄₅₆ = 10 years

Thus, time (T) = 10 years Answer