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 $7400 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5000

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

Amount (A) = $7400

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 = $7400 – $5000 = $2400

Thus, Simple Interest = $2400

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 × 2400}/_{5000 × 8}

= ²⁴⁰⁰⁰⁰/₄₀₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $2400 (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 $2400, then the time = ¹/₄₀₀ × 2400 years

= ^{1 × 2400}/₄₀₀ years

= ²⁴⁰⁰/₄₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.

(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 7% simple interest?

(4) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(5) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(6) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 3 years.

(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.

(9) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) If Jessica borrowed $3750 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.