Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

= ¹⁸⁰⁰⁰/₆₀₀₀

= 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) = $3000

Rate of Simple Interest (R) = 2% 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 = 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 $180, then the time = ¹/₆₀ × 180 years

= ^{1 × 180}/₆₀ years

= ¹⁸⁰/₆₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

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

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(4) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.

(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 7% simple interest?

(10) If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.