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 $8160 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6000

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

Amount (A) = $8160

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 = $8160 – $6000 = $2160

Thus, Simple Interest = $2160

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 × 2160}/_{6000 × 6}

= ²¹⁶⁰⁰⁰/₃₆₀₀₀

= 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) = $6000

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

Simple Interest = $2160 (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 $2160, then the time = ¹/₃₆₀ × 2160 years

= ^{1 × 2160}/₃₆₀ years

= ²¹⁶⁰/₃₆₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(10) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.