Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3538

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 = $3538 – $3050 = $488

Thus, Simple Interest = $488

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 × 488}/_{3050 × 4}

= ⁴⁸⁸⁰⁰/₁₂₂₀₀

= 4 years (using formula)

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

Simple Interest = $488 (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 $3050

= ⁴/₁₀₀ × 3050

= ^{4 × 3050}/₁₀₀

= ¹²²⁰⁰/₁₀₀ = 122

Thus, simple Interest for 1 year = $122

Now,

∵ If the simple Interest is $122, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₂ years

∴ If the simple Interest is $488, then the time = ¹/₁₂₂ × 488 years

= ^{1 × 488}/₁₂₂ years

= ⁴⁸⁸/₁₂₂ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 3% simple interest.

(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(6) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?

(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?

(9) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

(10) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.