Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12308

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 = $12308 – $6800 = $5508

Thus, Simple Interest = $5508

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 × 5508}/_{6800 × 9}

= ⁵⁵⁰⁸⁰⁰/₆₁₂₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 9% per annum

Simple Interest = $5508 (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 = 9% of Principal

= 9% of $6800

= ⁹/₁₀₀ × 6800

= ^{9 × 6800}/₁₀₀

= ⁶¹²⁰⁰/₁₀₀ = 612

Thus, simple Interest for 1 year = $612

Now,

∵ If the simple Interest is $612, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₂ years

∴ If the simple Interest is $5508, then the time = ¹/₆₁₂ × 5508 years

= ^{1 × 5508}/₆₁₂ years

= ⁵⁵⁰⁸/₆₁₂ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.

(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.

(5) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(6) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 3 years.

(9) Patricia had to pay $3433.5 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 James borrowed a sum of $5000 at 6% simple interest for 7 years.