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) How much loan did Thomas borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6960 to clear it?

(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7240 to clear the loan, then find the time period of the loan.

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?

(6) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(10) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?