Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $5440

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 = $5440 – $4000 = $1440

Thus, Simple Interest = $1440

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 × 1440}/_{4000 × 6}

= ¹⁴⁴⁰⁰⁰/₂₄₀₀₀

= 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) = $4000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $1440 (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 = 6% of Principal

= 6% of $4000

= ⁶/₁₀₀ × 4000

= ^{6 × 4000}/₁₀₀

= ²⁴⁰⁰⁰/₁₀₀ = 240

Thus, simple Interest for 1 year = $240

Now,

∵ If the simple Interest is $240, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₄₀ years

∴ If the simple Interest is $1440, then the time = ¹/₂₄₀ × 1440 years

= ^{1 × 1440}/₂₄₀ years

= ¹⁴⁴⁰/₂₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(3) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(6) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.

(7) 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.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.