Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $8800

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 = $8800 – $5500 = $3300

Thus, Simple Interest = $3300

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 × 3300}/_{5500 × 10}

= ³³⁰⁰⁰⁰/₅₅₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 10% per annum

Simple Interest = $3300 (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 $5500

= ¹⁰/₁₀₀ × 5500

= ^{10 × 5500}/₁₀₀

= ⁵⁵⁰⁰⁰/₁₀₀ = 550

Thus, simple Interest for 1 year = $550

Now,

∵ If the simple Interest is $550, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₀ years

∴ If the simple Interest is $3300, then the time = ¹/₅₅₀ × 3300 years

= ^{1 × 3300}/₅₅₀ years

= ³³⁰⁰/₅₅₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 4 years.

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 10% simple interest.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?

(8) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?

(10) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?