Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3286

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 = $3286 – $3100 = $186

Thus, Simple Interest = $186

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 × 186}/_{3100 × 3}

= ¹⁸⁶⁰⁰/₉₃₀₀

= 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) = $3100

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $186 (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 = 3% of Principal

= 3% of $3100

= ³/₁₀₀ × 3100

= ^{3 × 3100}/₁₀₀

= ⁹³⁰⁰/₁₀₀ = 93

Thus, simple Interest for 1 year = $93

Now,

∵ If the simple Interest is $93, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₃ years

∴ If the simple Interest is $186, then the time = ¹/₉₃ × 186 years

= ^{1 × 186}/₉₃ years

= ¹⁸⁶/₉₃ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(6) How much loan did Sharon borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9687.5 to clear it?

(7) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.

(8) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.