Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $6710

Rate of Simple Interest (R) = 2%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$6710 = P (1 + 2% × 5)

⇒ $6710 = P (1 + ²/₁₀₀ × 5)

⇒ $6710 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6710 = P (1 + ¹⁰/₁₀₀)

⇒ $6710 = P (^{100 + 10}/₁₀₀)

⇒ $6710 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6710

⇒ P = ⁶⁷¹⁰/_¹¹⁰/100

⇒ P = 6710 × ¹⁰⁰/₁₁₀

⇒ P = ^{6710 × 100}/₁₁₀

⇒ P = ⁶⁷¹⁰⁰⁰/₁₁₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 6710, then the Principal = ¹⁰⁰/₁₁₀ × 6710

= ^{100 × 6710}/₁₁₀

= ⁶⁷¹⁰⁰⁰/₁₁₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(2) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(3) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.

(7) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(9) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?

(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.