Simple Interest
Math MCQs

Question :    William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5000

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7800

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 = $7800 – $5000 = $2800

Thus, Simple Interest = $2800

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 × 2800}/_{5000 × 8}

= ²⁸⁰⁰⁰⁰/₄₀₀₀₀

= 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) = $5000

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2800 (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 = 8% of Principal

= 8% of $5000

= ⁸/₁₀₀ × 5000

= ^{8 × 5000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = 400

Thus, simple Interest for 1 year = $400

Now,

∵ If the simple Interest is $400, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₀ years

∴ If the simple Interest is $2800, then the time = ¹/₄₀₀ × 2800 years

= ^{1 × 2800}/₄₀₀ years

= ²⁸⁰⁰/₄₀₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(2) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $11220 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.

(6) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.

(7) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.