Simple Interest
MCQs Math

Question:     Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution And Explanation

Solution

Given,

Principal (P) = $6000

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

Amount (A) = $10800

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 = $10800 – $6000 = $4800

Thus, Simple Interest = $4800

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 × 4800}/_{6000 × 8}

= ⁴⁸⁰⁰⁰⁰/₄₈₀₀₀

= 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) = $6000

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

Simple Interest = $4800 (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 $6000

= ⁸/₁₀₀ × 6000

= ^{8 × 6000}/₁₀₀

= ⁴⁸⁰⁰⁰/₁₀₀ = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₀ years

∴ If the simple Interest is $4800, then the time = ¹/₄₈₀ × 4800 years

= ^{1 × 4800}/₄₈₀ years

= ⁴⁸⁰⁰/₄₈₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.

(2) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(4) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(7) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(8) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(9) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 3 years.