mcqs Math Simple Interest Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan. 8029

Question: Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 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) = $5100

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

Amount (A) = $10200

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10200 – $5100 = $5100

Thus, Simple Interest = $5100

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5100}/_{5100 × 10}

= ⁵¹⁰⁰⁰⁰/₅₁₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5100

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

Simple Interest = $5100 (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 $5100

= ¹⁰/₁₀₀ × 5100

= ^{10 × 5100}/₁₀₀

= ⁵¹⁰⁰⁰/₁₀₀ = 510

Thus, simple Interest for 1 year = $510

Now,

∵ If the simple Interest is $510, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₀ years

∴ If the simple Interest is $5100, then the time = ¹/₅₁₀ × 5100 years

= ^{1 × 5100}/₅₁₀ years

= ⁵¹⁰⁰/₅₁₀ = 10 years

Thus, time (T) = 10 years Answer