Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3410

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 = $3410 – $3100 = $310

Thus, Simple Interest = $310

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 × 310}/_{3100 × 5}

= ³¹⁰⁰⁰/₁₅₅₀₀

= 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) = 5% per annum

Simple Interest = $310 (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 = 5% of Principal

= 5% of $3100

= ⁵/₁₀₀ × 3100

= ^{5 × 3100}/₁₀₀

= ¹⁵⁵⁰⁰/₁₀₀ = 155

Thus, simple Interest for 1 year = $155

Now,

∵ If the simple Interest is $155, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₅ years

∴ If the simple Interest is $310, then the time = ¹/₁₅₅ × 310 years

= ^{1 × 310}/₁₅₅ years

= ³¹⁰/₁₅₅ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.

(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?

(4) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(6) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(9) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(10) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9676 to clear the loan, then find the time period of the loan.