Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $10440

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 = $10440 – $5800 = $4640

Thus, Simple Interest = $4640

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 × 4640}/_{5800 × 8}

= ⁴⁶⁴⁰⁰⁰/₄₆₄₀₀

= 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) = $5800

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

Simple Interest = $4640 (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 $5800

= ⁸/₁₀₀ × 5800

= ^{8 × 5800}/₁₀₀

= ⁴⁶⁴⁰⁰/₁₀₀ = 464

Thus, simple Interest for 1 year = $464

Now,

∵ If the simple Interest is $464, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₄ years

∴ If the simple Interest is $4640, then the time = ¹/₄₆₄ × 4640 years

= ^{1 × 4640}/₄₆₄ years

= ⁴⁶⁴⁰/₄₆₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Kevin borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8165 to clear it?

(2) If Matthew paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

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

(4) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.

(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 3% simple interest?

(6) If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.

(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?