Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $6864

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 = $6864 – $4400 = $2464

Thus, Simple Interest = $2464

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 × 2464}/_{4400 × 8}

= ²⁴⁶⁴⁰⁰/₃₅₂₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $4400

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

Simple Interest = $2464 (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 $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $2464, then the time = ¹/₃₅₂ × 2464 years

= ^{1 × 2464}/₃₅₂ years

= ²⁴⁶⁴/₃₅₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) 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.

(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.

(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(5) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.