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 $8584 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8584

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 = $8584 – $5800 = $2784

Thus, Simple Interest = $2784

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 × 2784}/_{5800 × 8}

= ²⁷⁸⁴⁰⁰/₄₆₄₀₀

= 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) = $5800

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

Simple Interest = $2784 (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 $2784, then the time = ¹/₄₆₄ × 2784 years

= ^{1 × 2784}/₄₆₄ years

= ²⁷⁸⁴/₄₆₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.

(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(4) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 4 years.

(6) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?

(8) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(9) Richard had to pay $3924 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.