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) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.

(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.

(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 4 years.

(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(6) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.