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) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.

(2) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.

(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(4) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(5) 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?

(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.

(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?