Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10030

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 = $10030 – $5900 = $4130

Thus, Simple Interest = $4130

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 × 4130}/_{5900 × 7}

= ⁴¹³⁰⁰⁰/₄₁₃₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $4130 (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 = 7% of Principal

= 7% of $5900

= ⁷/₁₀₀ × 5900

= ^{7 × 5900}/₁₀₀

= ⁴¹³⁰⁰/₁₀₀ = 413

Thus, simple Interest for 1 year = $413

Now,

∵ If the simple Interest is $413, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₃ years

∴ If the simple Interest is $4130, then the time = ¹/₄₁₃ × 4130 years

= ^{1 × 4130}/₄₁₃ years

= ⁴¹³⁰/₄₁₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(3) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?

(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(7) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?

(9) If William borrowed $3500 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.