Simple Interest
MCQs Math

Question:     Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9900

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 = $9900 – $5500 = $4400

Thus, Simple Interest = $4400

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 × 4400}/_{5500 × 8}

= ⁴⁴⁰⁰⁰⁰/₄₄₀₀₀

= 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) = $5500

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4400 (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 = 8% of Principal

= 8% of $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $4400, then the time = ¹/₄₄₀ × 4400 years

= ^{1 × 4400}/₄₄₀ years

= ⁴⁴⁰⁰/₄₄₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.

(5) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?

(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(7) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.

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

(9) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.