Simple Interest
Math MCQs

Question :    In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

Correct Answer  5

Solution & Explanation

Solution

Given,

Principal (P) = $3050

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

Amount (A) = $3660

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 = $3660 – $3050 = $610

Thus, Simple Interest = $610

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 × 610}/_{3050 × 4}

= ⁶¹⁰⁰⁰/₁₂₂₀₀

= 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) = $3050

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

Simple Interest = $610 (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 $3050

= ⁴/₁₀₀ × 3050

= ^{4 × 3050}/₁₀₀

= ¹²²⁰⁰/₁₀₀ = 122

Thus, simple Interest for 1 year = $122

Now,

∵ If the simple Interest is $122, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₁₂₂ years

∴ If the simple Interest is $610, then the time = ¹/₁₂₂ × 610 years

= ^{1 × 610}/₁₂₂ years

= ⁶¹⁰/₁₂₂ = 5 years

Thus, time (T) = 5 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7783 to clear the loan, then find the time period of the loan.

(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(4) 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.

(5) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?

(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(8) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(9) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.