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 $8791 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $8791

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 = $8791 – $5900 = $2891

Thus, Simple Interest = $2891

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 × 2891}/_{5900 × 7}

= ²⁸⁹¹⁰⁰/₄₁₃₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $2891 (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 $2891, then the time = ¹/₄₁₃ × 2891 years

= ^{1 × 2891}/₄₁₃ years

= ²⁸⁹¹/₄₁₃ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.

(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(6) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(7) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.