Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3233

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 = $3233 – $3050 = $183

Thus, Simple Interest = $183

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 × 183}/_{3050 × 2}

= ¹⁸³⁰⁰/₆₁₀₀

= 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) = $3050

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

Simple Interest = $183 (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 $3050

= ²/₁₀₀ × 3050

= ^{2 × 3050}/₁₀₀

= ⁶¹⁰⁰/₁₀₀ = 61

Thus, simple Interest for 1 year = $61

Now,

∵ If the simple Interest is $61, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁ years

∴ If the simple Interest is $183, then the time = ¹/₆₁ × 183 years

= ^{1 × 183}/₆₁ years

= ¹⁸³/₆₁ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.

(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.

(9) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.