Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 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) = 10% per annum

Amount (A) = $9600

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 = $9600 – $6000 = $3600

Thus, Simple Interest = $3600

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 × 3600}/_{6000 × 10}

= ³⁶⁰⁰⁰⁰/₆₀₀₀₀

= 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) = 10% per annum

Simple Interest = $3600 (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 = 10% of Principal

= 10% of $6000

= ¹⁰/₁₀₀ × 6000

= ^{10 × 6000}/₁₀₀

= ⁶⁰⁰⁰⁰/₁₀₀ = 600

Thus, simple Interest for 1 year = $600

Now,

∵ If the simple Interest is $600, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀₀ years

∴ If the simple Interest is $3600, then the time = ¹/₆₀₀ × 3600 years

= ^{1 × 3600}/₆₀₀ years

= ³⁶⁰⁰/₆₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 8% simple interest?

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?

(8) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

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