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 $11400 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6000

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

Amount (A) = $11400

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 = $11400 – $6000 = $5400

Thus, Simple Interest = $5400

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 × 5400}/_{6000 × 10}

= ⁵⁴⁰⁰⁰⁰/₆₀₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $5400 (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 $5400, then the time = ¹/₆₀₀ × 5400 years

= ^{1 × 5400}/₆₀₀ years

= ⁵⁴⁰⁰/₆₀₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 5% simple interest?

(2) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(7) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(8) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?

(9) Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?