Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $5680

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 = $5680 – $4000 = $1680

Thus, Simple Interest = $1680

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 × 1680}/_{4000 × 6}

= ¹⁶⁸⁰⁰⁰/₂₄₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1680 (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 $4000

= ⁶/₁₀₀ × 4000

= ^{6 × 4000}/₁₀₀

= ²⁴⁰⁰⁰/₁₀₀ = 240

Thus, simple Interest for 1 year = $240

Now,

∵ If the simple Interest is $240, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₀ years

∴ If the simple Interest is $1680, then the time = ¹/₂₄₀ × 1680 years

= ^{1 × 1680}/₂₄₀ years

= ¹⁶⁸⁰/₂₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(2) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 10% simple interest?

(3) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.

(5) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(7) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.

(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.