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 $8800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $8800

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 = $8800 – $4400 = $4400

Thus, Simple Interest = $4400

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 × 4400}/_{4400 × 10}

= ⁴⁴⁰⁰⁰⁰/₄₄₀₀₀

= 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) = $4400

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

Simple Interest = $4400 (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 $4400, then the time = ¹/₄₄₀ × 4400 years

= ^{1 × 4400}/₄₄₀ years

= ⁴⁴⁰⁰/₄₄₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.

(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(3) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(4) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 3 years.

(6) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?

(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(9) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.