Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 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) = 10% per annum

Amount (A) = $11800

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 = $11800 – $5900 = $5900

Thus, Simple Interest = $5900

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 × 5900}/_{5900 × 10}

= ⁵⁹⁰⁰⁰⁰/₅₉₀₀₀

= 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) = 10% per annum

Simple Interest = $5900 (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 = 10% of Principal

= 10% of $5900

= ¹⁰/₁₀₀ × 5900

= ^{10 × 5900}/₁₀₀

= ⁵⁹⁰⁰⁰/₁₀₀ = 590

Thus, simple Interest for 1 year = $590

Now,

∵ If the simple Interest is $590, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₀ years

∴ If the simple Interest is $5900, then the time = ¹/₅₉₀ × 5900 years

= ^{1 × 5900}/₅₉₀ years

= ⁵⁹⁰⁰/₅₉₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) 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.

(2) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 2% simple interest for 7 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 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) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(7) Mark had to pay $4664 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(10) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.