Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 4% 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 × 4}

= ⁶⁰⁰⁰⁰/₁₂₀₀₀

= 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) = 4% 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 = 4% of Principal

= 4% of $3000

= ⁴/₁₀₀ × 3000

= ^{4 × 3000}/₁₀₀

= ¹²⁰⁰⁰/₁₀₀ = 120

Thus, simple Interest for 1 year = $120

Now,

∵ If the simple Interest is $120, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₀ years

∴ If the simple Interest is $600, then the time = ¹/₁₂₀ × 600 years

= ^{1 × 600}/₁₂₀ years

= ⁶⁰⁰/₁₂₀ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(3) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $8704 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

(7) If John borrowed $3200 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 Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(9) How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?