Simple Interest
Math MCQs

Question :    Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9984

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 = $9984 – $6400 = $3584

Thus, Simple Interest = $3584

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 × 3584}/_{6400 × 7}

= ³⁵⁸⁴⁰⁰/₄₄₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 7% per annum

Simple Interest = $3584 (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 = 7% of Principal

= 7% of $6400

= ⁷/₁₀₀ × 6400

= ^{7 × 6400}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $3584, then the time = ¹/₄₄₈ × 3584 years

= ^{1 × 3584}/₄₄₈ years

= ³⁵⁸⁴/₄₄₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(2) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 4 years.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(5) 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.

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

(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(9) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.