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) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?

(3) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?

(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 4% simple interest?

(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $13400 to clear the loan, then find the time period of the loan.

(9) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.