Simple Interest
Math MCQs

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

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 4% 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 × 4}

= ²⁴⁰⁰⁰/₁₂₀₀₀

= 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) = 4% 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 = 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 $240, then the time = ¹/₁₂₀ × 240 years

= ^{1 × 240}/₁₂₀ years

= ²⁴⁰/₁₂₀ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.

(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(6) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.

(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.