Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 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) = 10% per annum

Amount (A) = $12540

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 = $12540 – $6600 = $5940

Thus, Simple Interest = $5940

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 × 5940}/_{6600 × 10}

= ⁵⁹⁴⁰⁰⁰/₆₆₀₀₀

= 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) = 10% per annum

Simple Interest = $5940 (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 = 10% of Principal

= 10% of $6600

= ¹⁰/₁₀₀ × 6600

= ^{10 × 6600}/₁₀₀

= ⁶⁶⁰⁰⁰/₁₀₀ = 660

Thus, simple Interest for 1 year = $660

Now,

∵ If the simple Interest is $660, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₆₀ years

∴ If the simple Interest is $5940, then the time = ¹/₆₆₀ × 5940 years

= ^{1 × 5940}/₆₆₀ years

= ⁵⁹⁴⁰/₆₆₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

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

(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(6) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $7616 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 if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.

(9) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(10) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.