Simple Interest
Math MCQs

Question :    In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3100

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

= ³¹⁰⁰⁰/₆₂₀₀

= 5 years (using formula)

Thus, Time (T) = 5 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 = $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 = 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 $310, then the time = ¹/₆₂ × 310 years

= ^{1 × 310}/₆₂ years

= ³¹⁰/₆₂ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 7% simple interest?

(2) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

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

(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8856 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.

(10) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.