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 $9720 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $9720

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 = $9720 – $5400 = $4320

Thus, Simple Interest = $4320

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 × 4320}/_{5400 × 10}

= ⁴³²⁰⁰⁰/₅₄₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $4320 (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 $4320, then the time = ¹/₅₄₀ × 4320 years

= ^{1 × 4320}/₅₄₀ years

= ⁴³²⁰/₅₄₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.

(4) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(8) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(10) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?