Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4100

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $7790

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 = $7790 – $4100 = $3690

Thus, Simple Interest = $3690

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 × 3690}/_{4100 × 10}

= ³⁶⁹⁰⁰⁰/₄₁₀₀₀

= 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) = $4100

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3690 (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 = 10% of Principal

= 10% of $4100

= ¹⁰/₁₀₀ × 4100

= ^{10 × 4100}/₁₀₀

= ⁴¹⁰⁰⁰/₁₀₀ = 410

Thus, simple Interest for 1 year = $410

Now,

∵ If the simple Interest is $410, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₀ years

∴ If the simple Interest is $3690, then the time = ¹/₄₁₀ × 3690 years

= ^{1 × 3690}/₄₁₀ years

= ³⁶⁹⁰/₄₁₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) 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.

(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(6) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(9) Mary had to pay $3233 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.