Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7040

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 = $7040 – $4400 = $2640

Thus, Simple Interest = $2640

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 × 2640}/_{4400 × 10}

= ²⁶⁴⁰⁰⁰/₄₄₀₀₀

= 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) = $4400

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

Simple Interest = $2640 (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 $4400

= ¹⁰/₁₀₀ × 4400

= ^{10 × 4400}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $2640, then the time = ¹/₄₄₀ × 2640 years

= ^{1 × 2640}/₄₄₀ years

= ²⁶⁴⁰/₄₄₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?

(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.

(3) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.

(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

(6) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

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

(9) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(10) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.