Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6000

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

Amount (A) = $9600

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 = $9600 – $6000 = $3600

Thus, Simple Interest = $3600

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 × 3600}/_{6000 × 10}

= ³⁶⁰⁰⁰⁰/₆₀₀₀₀

= 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) = $6000

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

Simple Interest = $3600 (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 $6000

= ¹⁰/₁₀₀ × 6000

= ^{10 × 6000}/₁₀₀

= ⁶⁰⁰⁰⁰/₁₀₀ = 600

Thus, simple Interest for 1 year = $600

Now,

∵ If the simple Interest is $600, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₀ years

∴ If the simple Interest is $3600, then the time = ¹/₆₀₀ × 3600 years

= ^{1 × 3600}/₆₀₀ years

= ³⁶⁰⁰/₆₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?

(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.

(3) How much loan did Richard borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6440 to clear it?

(4) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?

(7) Ashley had to pay $4823 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.