Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3000

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

Amount (A) = $3600

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 = $3600 – $3000 = $600

Thus, Simple Interest = $600

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 × 600}/_{3000 × 5}

= ⁶⁰⁰⁰⁰/₁₅₀₀₀

= 4 years (using formula)

Thus, Time (T) = 4 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 = $600 (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 $600, then the time = ¹/₁₅₀ × 600 years

= ^{1 × 600}/₁₅₀ years

= ⁶⁰⁰/₁₅₀ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

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

(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(8) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(9) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.