Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?

Correct Answer  3

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 5% per annum

Amount (A) = $3450

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 = $3450 – $3000 = $450

Thus, Simple Interest = $450

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 × 450}/_{3000 × 5}

= ⁴⁵⁰⁰⁰/₁₅₀₀₀

= 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) = 5% per annum

Simple Interest = $450 (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 = 5% of Principal

= 5% of $3000

= ⁵/₁₀₀ × 3000

= ^{5 × 3000}/₁₀₀

= ¹⁵⁰⁰⁰/₁₀₀ = 150

Thus, simple Interest for 1 year = $150

Now,

∵ If the simple Interest is $150, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₅₀ years

∴ If the simple Interest is $450, then the time = ¹/₁₅₀ × 450 years

= ^{1 × 450}/₁₅₀ years

= ⁴⁵⁰/₁₅₀ = 3 years

Thus, time (T) = 3 years Answer

Similar Questions

(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?

(2) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.

(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(6) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?

(9) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 6% simple interest.