Simple Interest
Math MCQs

Question :    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.

Correct Answer  $3150

Solution & Explanation

Solution

Given,

Amount (A) = $3528

Rate of Simple Interest (R) = 4%

Time (T) = 3 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

$3528 = P (1 + 4% × 3)

⇒ $3528 = P (1 + ⁴/₁₀₀ × 3)

⇒ $3528 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $3528 = P (1 + ¹²/₁₀₀)

⇒ $3528 = P (^{100 + 12}/₁₀₀)

⇒ $3528 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $3528

⇒ P = ³⁵²⁸/_¹¹²/100

⇒ P = 3528 × ¹⁰⁰/₁₁₂

⇒ P = ^{3528 × 100}/₁₁₂

⇒ P = ³⁵²⁸⁰⁰/₁₁₂

⇒ P = $3150

Thus, the sum borrowed (P) = $3150 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 3528, then the Principal = ¹⁰⁰/₁₁₂ × 3528

= ^{100 × 3528}/₁₁₂

= ³⁵²⁸⁰⁰/₁₁₂

= 3150

Thus, Principal = $3150

Thus, the sum borrowed = $3150 Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.

(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?

(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.

(7) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

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

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(10) David had to pay $3910 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.