Simple Interest
Math MCQs

Question :    How much loan did Patricia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5922.5 to clear it?

Correct Answer  $5150

Solution & Explanation

Solution

Given,

Amount (A) = $5922.5

Rate of Simple Interest (R) = 3%

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

$5922.5 = P (1 + 3% × 5)

⇒ $5922.5 = P (1 + ³/₁₀₀ × 5)

⇒ $5922.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $5922.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5922.5 = P (^{100 + 15}/₁₀₀)

⇒ $5922.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5922.5

⇒ P = ^5922.5/_¹¹⁵/100

⇒ P = 5922.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5922.5 × 100}/₁₁₅

⇒ P = ⁵⁹²²⁵⁰/₁₁₅

⇒ P = $5150

Thus, the sum borrowed (P) = $5150 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 5922.5, then the Principal = ¹⁰⁰/₁₁₅ × 5922.5

= ^{100 × 5922.5}/₁₁₅

= ⁵⁹²²⁵⁰/₁₁₅

= 5150

Thus, Principal = $5150

Thus, the sum borrowed = $5150 Answer

Similar Questions

(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 4 years.

(2) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

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

(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?

(6) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?

(9) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.