Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7844

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 = $7844 – $5300 = $2544

Thus, Simple Interest = $2544

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 × 2544}/_{5300 × 8}

= ²⁵⁴⁴⁰⁰/₄₂₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5300

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2544 (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 = 8% of Principal

= 8% of $5300

= ⁸/₁₀₀ × 5300

= ^{8 × 5300}/₁₀₀

= ⁴²⁴⁰⁰/₁₀₀ = 424

Thus, simple Interest for 1 year = $424

Now,

∵ If the simple Interest is $424, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₄ years

∴ If the simple Interest is $2544, then the time = ¹/₄₂₄ × 2544 years

= ^{1 × 2544}/₄₂₄ years

= ²⁵⁴⁴/₄₂₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(5) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(9) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.