mcqs Math Simple Interest Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan. 8006

Question: Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 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) = 9% per annum

Amount (A) = $11210

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11210 – $5900 = $5310

Thus, Simple Interest = $5310

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5310}/_{5900 × 9}

= ⁵³¹⁰⁰⁰/₅₃₁₀₀

= 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) = 9% per annum

Simple Interest = $5310 (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 = 9% of Principal

= 9% of $5900

= ⁹/₁₀₀ × 5900

= ^{9 × 5900}/₁₀₀

= ⁵³¹⁰⁰/₁₀₀ = 531

Thus, simple Interest for 1 year = $531

Now,

∵ If the simple Interest is $531, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₃₁ years

∴ If the simple Interest is $5310, then the time = ¹/₅₃₁ × 5310 years

= ^{1 × 5310}/₅₃₁ years

= ⁵³¹⁰/₅₃₁ = 10 years

Thus, time (T) = 10 years Answer