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) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(9) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.