Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9780

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9780 – $6000 = $3780

Thus, Simple Interest = $3780

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3780}/_{6000 × 7}

= ³⁷⁸⁰⁰⁰/₄₂₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3780 (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 = 7% of Principal

= 7% of $6000

= ⁷/₁₀₀ × 6000

= ^{7 × 6000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3780, then the time = ¹/₄₂₀ × 3780 years

= ^{1 × 3780}/₄₂₀ years

= ³⁷⁸⁰/₄₂₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.

(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(5) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.

(6) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(7) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

(9) If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.