mcqs Math Simple Interest Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan. 8030

Question: Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 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) = $5200

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

Amount (A) = $10400

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10400 – $5200 = $5200

Thus, Simple Interest = $5200

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5200}/_{5200 × 10}

= ⁵²⁰⁰⁰⁰/₅₂₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5200

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

Simple Interest = $5200 (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 $5200

= ¹⁰/₁₀₀ × 5200

= ^{10 × 5200}/₁₀₀

= ⁵²⁰⁰⁰/₁₀₀ = 520

Thus, simple Interest for 1 year = $520

Now,

∵ If the simple Interest is $520, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₀ years

∴ If the simple Interest is $5200, then the time = ¹/₅₂₀ × 5200 years

= ^{1 × 5200}/₅₂₀ years

= ⁵²⁰⁰/₅₂₀ = 10 years

Thus, time (T) = 10 years Answer