mcqs Math Simple Interest Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan. 7711

Question: Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(A)  6
(B)  10
(C)  8
(D)  12

Correct Answer 8

Solution And Explanation

Solution

Given,

Principal (P) = $4300

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

Amount (A) = $7740

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7740 – $4300 = $3440

Thus, Simple Interest = $3440

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3440}/_{4300 × 10}

= ³⁴⁴⁰⁰⁰/₄₃₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $4300

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

Simple Interest = $3440 (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 $4300

= ¹⁰/₁₀₀ × 4300

= ^{10 × 4300}/₁₀₀

= ⁴³⁰⁰⁰/₁₀₀ = 430

Thus, simple Interest for 1 year = $430

Now,

∵ If the simple Interest is $430, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₀ years

∴ If the simple Interest is $3440, then the time = ¹/₄₃₀ × 3440 years

= ^{1 × 3440}/₄₃₀ years

= ³⁴⁴⁰/₄₃₀ = 8 years

Thus, time (T) = 8 years Answer