Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3600

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 = $3600 – $3000 = $600

Thus, Simple Interest = $600

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 × 600}/_{3000 × 4}

= ⁶⁰⁰⁰⁰/₁₂₀₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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) = 4% per annum

Simple Interest = $600 (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 = 4% of Principal

= 4% of $3000

= ⁴/₁₀₀ × 3000

= ^{4 × 3000}/₁₀₀

= ¹²⁰⁰⁰/₁₀₀ = 120

Thus, simple Interest for 1 year = $120

Now,

∵ If the simple Interest is $120, then the time = 1 year

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

∴ If the simple Interest is $600, then the time = ¹/₁₂₀ × 600 years

= ^{1 × 600}/₁₂₀ years

= ⁶⁰⁰/₁₂₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

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

(3) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(4) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(7) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.