Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11084

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 = $11084 – $6800 = $4284

Thus, Simple Interest = $4284

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 × 4284}/_{6800 × 9}

= ⁴²⁸⁴⁰⁰/₆₁₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $6800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4284 (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 = 9% of Principal

= 9% of $6800

= ⁹/₁₀₀ × 6800

= ^{9 × 6800}/₁₀₀

= ⁶¹²⁰⁰/₁₀₀ = 612

Thus, simple Interest for 1 year = $612

Now,

∵ If the simple Interest is $612, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₂ years

∴ If the simple Interest is $4284, then the time = ¹/₆₁₂ × 4284 years

= ^{1 × 4284}/₆₁₂ years

= ⁴²⁸⁴/₆₁₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(6) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(7) 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.

(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(9) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.