Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $8360

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 = $8360 – $4400 = $3960

Thus, Simple Interest = $3960

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 × 3960}/_{4400 × 9}

= ³⁹⁶⁰⁰⁰/₃₉₆₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = 9% per annum

Simple Interest = $3960 (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 $4400

= ⁹/₁₀₀ × 4400

= ^{9 × 4400}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $3960, then the time = ¹/₃₉₆ × 3960 years

= ^{1 × 3960}/₃₉₆ years

= ³⁹⁶⁰/₃₉₆ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(3) 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.

(4) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.

(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(9) Paul had to pay $5405 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?