Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $10758

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 = $10758 – $6600 = $4158

Thus, Simple Interest = $4158

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 × 4158}/_{6600 × 7}

= ⁴¹⁵⁸⁰⁰/₄₆₂₀₀

= 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) = $6600

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

Simple Interest = $4158 (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 $6600

= ⁷/₁₀₀ × 6600

= ^{7 × 6600}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀ = 462

Thus, simple Interest for 1 year = $462

Now,

∵ If the simple Interest is $462, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₂ years

∴ If the simple Interest is $4158, then the time = ¹/₄₆₂ × 4158 years

= ^{1 × 4158}/₄₆₂ years

= ⁴¹⁵⁸/₄₆₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(3) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.

(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.