Simple Interest
Math MCQs

Question :    Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4200

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $6216

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 = $6216 – $4200 = $2016

Thus, Simple Interest = $2016

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 × 2016}/_{4200 × 8}

= ²⁰¹⁶⁰⁰/₃₃₆₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $4200

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2016 (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 = 8% of Principal

= 8% of $4200

= ⁸/₁₀₀ × 4200

= ^{8 × 4200}/₁₀₀

= ³³⁶⁰⁰/₁₀₀ = 336

Thus, simple Interest for 1 year = $336

Now,

∵ If the simple Interest is $336, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₃₆ years

∴ If the simple Interest is $2016, then the time = ¹/₃₃₆ × 2016 years

= ^{1 × 2016}/₃₃₆ years

= ²⁰¹⁶/₃₃₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(2) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.

(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(6) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.

(9) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?

(10) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.