Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $7600

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 = $7600 – $4000 = $3600

Thus, Simple Interest = $3600

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 × 3600}/_{4000 × 9}

= ³⁶⁰⁰⁰⁰/₃₆₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 9% per annum

Simple Interest = $3600 (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 $4000

= ⁹/₁₀₀ × 4000

= ^{9 × 4000}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $3600, then the time = ¹/₃₆₀ × 3600 years

= ^{1 × 3600}/₃₆₀ years

= ³⁶⁰⁰/₃₆₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?

(8) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(10) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.