Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8195

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

$8195 = P (1 + 2% × 5)

⇒ $8195 = P (1 + ²/₁₀₀ × 5)

⇒ $8195 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8195 = P (1 + ¹⁰/₁₀₀)

⇒ $8195 = P (^{100 + 10}/₁₀₀)

⇒ $8195 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8195

⇒ P = ⁸¹⁹⁵/_¹¹⁰/100

⇒ P = 8195 × ¹⁰⁰/₁₁₀

⇒ P = ^{8195 × 100}/₁₁₀

⇒ P = ⁸¹⁹⁵⁰⁰/₁₁₀

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 8195, then the Principal = ¹⁰⁰/₁₁₀ × 8195

= ^{100 × 8195}/₁₁₀

= ⁸¹⁹⁵⁰⁰/₁₁₀

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.

(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?

(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(10) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.