Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8640

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 = $8640 – $5400 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{5400 × 10}

= ³²⁴⁰⁰⁰/₅₄₀₀₀

= 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) = $5400

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3240 (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 = 10% of Principal

= 10% of $5400

= ¹⁰/₁₀₀ × 5400

= ^{10 × 5400}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $3240, then the time = ¹/₅₄₀ × 3240 years

= ^{1 × 3240}/₅₄₀ years

= ³²⁴⁰/₅₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?

(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.