Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 2% per annum

Amount (A) = $3224

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 = $3224 – $3100 = $124

Thus, Simple Interest = $124

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 × 124}/_{3100 × 2}

= ¹²⁴⁰⁰/₆₂₀₀

= 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) = 2% per annum

Simple Interest = $124 (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 = 2% of Principal

= 2% of $3100

= ²/₁₀₀ × 3100

= ^{2 × 3100}/₁₀₀

= ⁶²⁰⁰/₁₀₀ = 62

Thus, simple Interest for 1 year = $62

Now,

∵ If the simple Interest is $62, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂ years

∴ If the simple Interest is $124, then the time = ¹/₆₂ × 124 years

= ^{1 × 124}/₆₂ years

= ¹²⁴/₆₂ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.

(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.

(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

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

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

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

(10) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.