Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3240

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 = $3240 – $3000 = $240

Thus, Simple Interest = $240

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 × 240}/_{3000 × 2}

= ²⁴⁰⁰⁰/₆₀₀₀

= 4 years (using formula)

Thus, Time (T) = 4 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 = $240 (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 $240, then the time = ¹/₆₀ × 240 years

= ^{1 × 240}/₆₀ years

= ²⁴⁰/₆₀ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(2) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(5) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?

(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(8) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?

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

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 6% simple interest for 8 years.