Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 8% 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  9

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 8% 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 × 8}

= ⁴⁵³⁶⁰⁰/₅₀₄₀₀

= 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) = $6300

Rate of Simple Interest (R) = 8% 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 = 8% of Principal

= 8% of $6300

= ⁸/₁₀₀ × 6300

= ^{8 × 6300}/₁₀₀

= ⁵⁰⁴⁰⁰/₁₀₀ = 504

Thus, simple Interest for 1 year = $504

Now,

∵ If the simple Interest is $504, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₀₄ years

∴ If the simple Interest is $4536, then the time = ¹/₅₀₄ × 4536 years

= ^{1 × 4536}/₅₀₄ years

= ⁴⁵³⁶/₅₀₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(3) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(9) If David paid $3808 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.