Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3300

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 = $3300 – $3000 = $300

Thus, Simple Interest = $300

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 × 300}/_{3000 × 2}

= ³⁰⁰⁰⁰/₆₀₀₀

= 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) = $3000

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

Simple Interest = $300 (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 $3000

= ²/₁₀₀ × 3000

= ^{2 × 3000}/₁₀₀

= ⁶⁰⁰⁰/₁₀₀ = 60

Thus, simple Interest for 1 year = $60

Now,

∵ If the simple Interest is $60, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₀ years

∴ If the simple Interest is $300, then the time = ¹/₆₀ × 300 years

= ^{1 × 300}/₆₀ years

= ³⁰⁰/₆₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 5% simple interest?

(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(3) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.

(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(10) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 7% simple interest?