mcqs Math Simple Interest Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan. 7905

Question: Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 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) = 6% per annum

Amount (A) = $8160

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8160 – $5100 = $3060

Thus, Simple Interest = $3060

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3060}/_{5100 × 6}

= ³⁰⁶⁰⁰⁰/₃₀₆₀₀

= 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) = 6% per annum

Simple Interest = $3060 (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 = 6% of Principal

= 6% of $5100

= ⁶/₁₀₀ × 5100

= ^{6 × 5100}/₁₀₀

= ³⁰⁶⁰⁰/₁₀₀ = 306

Thus, simple Interest for 1 year = $306

Now,

∵ If the simple Interest is $306, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₆ years

∴ If the simple Interest is $3060, then the time = ¹/₃₀₆ × 3060 years

= ^{1 × 3060}/₃₀₆ years

= ³⁰⁶⁰/₃₀₆ = 10 years

Thus, time (T) = 10 years Answer