Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6300

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

Amount (A) = $10836

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 = $10836 – $6300 = $4536

Thus, Simple Interest = $4536

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 × 4536}/_{6300 × 9}

= ⁴⁵³⁶⁰⁰/₅₆₇₀₀

= 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) = $6300

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

Simple Interest = $4536 (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 $6300

= ⁹/₁₀₀ × 6300

= ^{9 × 6300}/₁₀₀

= ⁵⁶⁷⁰⁰/₁₀₀ = 567

Thus, simple Interest for 1 year = $567

Now,

∵ If the simple Interest is $567, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₇ years

∴ If the simple Interest is $4536, then the time = ¹/₅₆₇ × 4536 years

= ^{1 × 4536}/₅₆₇ years

= ⁴⁵³⁶/₅₆₇ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

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

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.

(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(7) 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.

(8) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.

(10) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.