Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6808

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 = $6808 – $4600 = $2208

Thus, Simple Interest = $2208

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 × 2208}/_{4600 × 6}

= ²²⁰⁸⁰⁰/₂₇₆₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4600

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2208 (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 = 6% of Principal

= 6% of $4600

= ⁶/₁₀₀ × 4600

= ^{6 × 4600}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = 276

Thus, simple Interest for 1 year = $276

Now,

∵ If the simple Interest is $276, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₆ years

∴ If the simple Interest is $2208, then the time = ¹/₂₇₆ × 2208 years

= ^{1 × 2208}/₂₇₆ years

= ²²⁰⁸/₂₇₆ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.

(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.

(5) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(6) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(9) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.