Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3120

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 = $3120 – $3000 = $120

Thus, Simple Interest = $120

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 × 120}/_{3000 × 2}

= ¹²⁰⁰⁰/₆₀₀₀

= 2 years (using formula)

Thus, Time (T) = 2 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) = $3000

Rate of Simple Interest (R) = 2% per annum

Simple Interest = $120 (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 = 2% of Principal

= 2% of $3000

= ²/₁₀₀ × 3000

= ^{2 × 3000}/₁₀₀

= ⁶⁰⁰⁰/₁₀₀ = 60

Thus, simple Interest for 1 year = $60

Now,

∵ If the simple Interest is $60, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀ years

∴ If the simple Interest is $120, then the time = ¹/₆₀ × 120 years

= ^{1 × 120}/₆₀ years

= ¹²⁰/₆₀ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.

(2) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.

(5) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(6) 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.

(7) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.