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) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.

(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(5) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.

(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(7) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) In how much time a principal of $3200 will amount to $3456 at a simple interest of 2% per annum?

(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(10) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.