Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $11520

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 = $11520 – $6400 = $5120

Thus, Simple Interest = $5120

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 × 5120}/_{6400 × 8}

= ⁵¹²⁰⁰⁰/₅₁₂₀₀

= 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) = $6400

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $5120 (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 = 8% of Principal

= 8% of $6400

= ⁸/₁₀₀ × 6400

= ^{8 × 6400}/₁₀₀

= ⁵¹²⁰⁰/₁₀₀ = 512

Thus, simple Interest for 1 year = $512

Now,

∵ If the simple Interest is $512, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₂ years

∴ If the simple Interest is $5120, then the time = ¹/₅₁₂ × 5120 years

= ^{1 × 5120}/₅₁₂ years

= ⁵¹²⁰/₅₁₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(5) If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) If Kimberly paid $5580 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.