Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $10260

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 = $10260 – $5400 = $4860

Thus, Simple Interest = $4860

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 × 4860}/_{5400 × 9}

= ⁴⁸⁶⁰⁰⁰/₄₈₆₀₀

= 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) = $5400

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

Simple Interest = $4860 (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 $5400

= ⁹/₁₀₀ × 5400

= ^{9 × 5400}/₁₀₀

= ⁴⁸⁶⁰⁰/₁₀₀ = 486

Thus, simple Interest for 1 year = $486

Now,

∵ If the simple Interest is $486, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₆ years

∴ If the simple Interest is $4860, then the time = ¹/₄₈₆ × 4860 years

= ^{1 × 4860}/₄₈₆ years

= ⁴⁸⁶⁰/₄₈₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.

(3) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 9% simple interest?