Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $10430

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 = $10430 – $7000 = $3430

Thus, Simple Interest = $3430

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 × 3430}/_{7000 × 7}

= ³⁴³⁰⁰⁰/₄₉₀₀₀

= 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) = $7000

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

Simple Interest = $3430 (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 $7000

= ⁷/₁₀₀ × 7000

= ^{7 × 7000}/₁₀₀

= ⁴⁹⁰⁰⁰/₁₀₀ = 490

Thus, simple Interest for 1 year = $490

Now,

∵ If the simple Interest is $490, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₀ years

∴ If the simple Interest is $3430, then the time = ¹/₄₉₀ × 3430 years

= ^{1 × 3430}/₄₉₀ years

= ³⁴³⁰/₄₉₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(2) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

(3) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(6) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.