Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3472 at a simple interest of 4% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3100

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

Amount (A) = $3472

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 = $3472 – $3100 = $372

Thus, Simple Interest = $372

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 × 372}/_{3100 × 4}

= ³⁷²⁰⁰/₁₂₄₀₀

= 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) = $3100

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

Simple Interest = $372 (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 $3100

= ⁴/₁₀₀ × 3100

= ^{4 × 3100}/₁₀₀

= ¹²⁴⁰⁰/₁₀₀ = 124

Thus, simple Interest for 1 year = $124

Now,

∵ If the simple Interest is $124, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₄ years

∴ If the simple Interest is $372, then the time = ¹/₁₂₄ × 372 years

= ^{1 × 372}/₁₂₄ years

= ³⁷²/₁₂₄ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 8 years.

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

(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(4) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(6) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(8) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(9) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.