Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3450

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 = $3450 – $3000 = $450

Thus, Simple Interest = $450

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 × 450}/_{3000 × 3}

= ⁴⁵⁰⁰⁰/₉₀₀₀

= 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) = 3% per annum

Simple Interest = $450 (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 $450, then the time = ¹/₉₀ × 450 years

= ^{1 × 450}/₉₀ years

= ⁴⁵⁰/₉₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 4 years.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

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

(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.

(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(6) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(8) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(10) If Christopher paid $4640 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.