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) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.

(2) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(4) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 2% simple interest?

(8) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.

(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.