Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

Correct Answer  2

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 3% per annum

Amount (A) = $3180

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 = $3180 – $3000 = $180

Thus, Simple Interest = $180

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 × 180}/_{3000 × 3}

= ¹⁸⁰⁰⁰/₉₀₀₀

= 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) = $3000

Rate of Simple Interest (R) = 3% per annum

Simple Interest = $180 (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 $3000

= ³/₁₀₀ × 3000

= ^{3 × 3000}/₁₀₀

= ⁹⁰⁰⁰/₁₀₀ = 90

Thus, simple Interest for 1 year = $90

Now,

∵ If the simple Interest is $90, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₉₀ years

∴ If the simple Interest is $180, then the time = ¹/₉₀ × 180 years

= ^{1 × 180}/₉₀ years

= ¹⁸⁰/₉₀ = 2 years

Thus, time (T) = 2 years Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(3) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(5) If Christopher paid $4800 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(8) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 4% simple interest?

(9) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.