Simple Interest
Math MCQs

Question :    In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

Correct Answer  4

Solution & Explanation

Solution

Given,

Principal (P) = $3000

Rate of Simple Interest (R) = 4% per annum

Amount (A) = $3480

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 = $3480 – $3000 = $480

Thus, Simple Interest = $480

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 × 480}/_{3000 × 4}

= ⁴⁸⁰⁰⁰/₁₂₀₀₀

= 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) = 4% per annum

Simple Interest = $480 (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 $480, then the time = ¹/₁₂₀ × 480 years

= ^{1 × 480}/₁₂₀ years

= ⁴⁸⁰/₁₂₀ = 4 years

Thus, time (T) = 4 years Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(5) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(6) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 5% simple interest?