Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3270

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 = $3270 – $3000 = $270

Thus, Simple Interest = $270

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 × 270}/_{3000 × 3}

= ²⁷⁰⁰⁰/₉₀₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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) = 3% per annum

Simple Interest = $270 (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 = 3% of Principal

= 3% of $3000

= ³/₁₀₀ × 3000

= ^{3 × 3000}/₁₀₀

= ⁹⁰⁰⁰/₁₀₀ = 90

Thus, simple Interest for 1 year = $90

Now,

∵ If the simple Interest is $90, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₀ years

∴ If the simple Interest is $270, then the time = ¹/₉₀ × 270 years

= ^{1 × 270}/₉₀ years

= ²⁷⁰/₉₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% 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 $7224 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?

(6) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(9) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(10) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.