mcqs Math Simple Interest Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan. 8025

Question: Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 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) = $4700

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

Amount (A) = $9400

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9400 – $4700 = $4700

Thus, Simple Interest = $4700

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4700}/_{4700 × 10}

= ⁴⁷⁰⁰⁰⁰/₄₇₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $4700

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

Simple Interest = $4700 (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 $4700

= ¹⁰/₁₀₀ × 4700

= ^{10 × 4700}/₁₀₀

= ⁴⁷⁰⁰⁰/₁₀₀ = 470

Thus, simple Interest for 1 year = $470

Now,

∵ If the simple Interest is $470, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₀ years

∴ If the simple Interest is $4700, then the time = ¹/₄₇₀ × 4700 years

= ^{1 × 4700}/₄₇₀ years

= ⁴⁷⁰⁰/₄₇₀ = 10 years

Thus, time (T) = 10 years Answer