mcqs Math Simple Interest Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan. 7975

Question: Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 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) = $5900

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

Amount (A) = $10620

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10620 – $5900 = $4720

Thus, Simple Interest = $4720

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4720}/_{5900 × 8}

= ⁴⁷²⁰⁰⁰/₄₇₂₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $5900

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

Simple Interest = $4720 (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 $5900

= ⁸/₁₀₀ × 5900

= ^{8 × 5900}/₁₀₀

= ⁴⁷²⁰⁰/₁₀₀ = 472

Thus, simple Interest for 1 year = $472

Now,

∵ If the simple Interest is $472, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₂ years

∴ If the simple Interest is $4720, then the time = ¹/₄₇₂ × 4720 years

= ^{1 × 4720}/₄₇₂ years

= ⁴⁷²⁰/₄₇₂ = 10 years

Thus, time (T) = 10 years Answer