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 $11900 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $11900

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 = $11900 – $7000 = $4900

Thus, Simple Interest = $4900

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 × 4900}/_{7000 × 7}

= ⁴⁹⁰⁰⁰⁰/₄₉₀₀₀

= 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) = $7000

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

Simple Interest = $4900 (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 $4900, then the time = ¹/₄₉₀ × 4900 years

= ^{1 × 4900}/₄₉₀ years

= ⁴⁹⁰⁰/₄₉₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 3 years.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.

(3) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(5) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(6) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(7) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) If Linda paid $4020 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 4 years.