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) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.

(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 9% simple interest?

(8) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?

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

(10) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.