Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3100

Rate of Simple Interest (R) = 2% 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 × 2}

= ¹⁸⁶⁰⁰/₆₂₀₀

= 3 years (using formula)

Thus, Time (T) = 3 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 = $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 = 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 $186, then the time = ¹/₆₂ × 186 years

= ^{1 × 186}/₆₂ years

= ¹⁸⁶/₆₂ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.

(3) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(4) How much loan did Jason borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8855 to clear it?

(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.

(7) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.

(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?