Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9780

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 = $9780 – $6000 = $3780

Thus, Simple Interest = $3780

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 × 3780}/_{6000 × 9}

= ³⁷⁸⁰⁰⁰/₅₄₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 9% per annum

Simple Interest = $3780 (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 = 9% of Principal

= 9% of $6000

= ⁹/₁₀₀ × 6000

= ^{9 × 6000}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $3780, then the time = ¹/₅₄₀ × 3780 years

= ^{1 × 3780}/₅₄₀ years

= ³⁷⁸⁰/₅₄₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(2) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.

(5) How much loan did Emily borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8437.5 to clear it?

(6) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.

(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(9) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.