Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8880

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 = $8880 – $6000 = $2880

Thus, Simple Interest = $2880

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 × 2880}/_{6000 × 6}

= ²⁸⁸⁰⁰⁰/₃₆₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $6000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2880 (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 = 6% of Principal

= 6% of $6000

= ⁶/₁₀₀ × 6000

= ^{6 × 6000}/₁₀₀

= ³⁶⁰⁰⁰/₁₀₀ = 360

Thus, simple Interest for 1 year = $360

Now,

∵ If the simple Interest is $360, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₀ years

∴ If the simple Interest is $2880, then the time = ¹/₃₆₀ × 2880 years

= ^{1 × 2880}/₃₆₀ years

= ²⁸⁸⁰/₃₆₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

(2) If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?

(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.

(6) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.

(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(10) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.