Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10880

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 = $10880 – $6800 = $4080

Thus, Simple Interest = $4080

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 × 4080}/_{6800 × 10}

= ⁴⁰⁸⁰⁰⁰/₆₈₀₀₀

= 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) = $6800

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

Simple Interest = $4080 (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 $6800

= ¹⁰/₁₀₀ × 6800

= ^{10 × 6800}/₁₀₀

= ⁶⁸⁰⁰⁰/₁₀₀ = 680

Thus, simple Interest for 1 year = $680

Now,

∵ If the simple Interest is $680, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₈₀ years

∴ If the simple Interest is $4080, then the time = ¹/₆₈₀ × 4080 years

= ^{1 × 4080}/₆₈₀ years

= ⁴⁰⁸⁰/₆₈₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

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

(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.

(4) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

(5) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?

(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.

(10) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?