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) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?

(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.

(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?

(8) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?

(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.