Simple Interest
Math MCQs

Question :    Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $4929

Rate of Simple Interest (R) = 2%

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

$4929 = P (1 + 2% × 3)

⇒ $4929 = P (1 + ²/₁₀₀ × 3)

⇒ $4929 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4929 = P (1 + ⁶/₁₀₀)

⇒ $4929 = P (^{100 + 6}/₁₀₀)

⇒ $4929 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4929

⇒ P = ⁴⁹²⁹/_¹⁰⁶/100

⇒ P = 4929 × ¹⁰⁰/₁₀₆

⇒ P = ^{4929 × 100}/₁₀₆

⇒ P = ⁴⁹²⁹⁰⁰/₁₀₆

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 = 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 × 2 = 6

Thus, simple interest for 3 years = 6

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 6 = 106

Calculation of the Principal

Now,

∵ If the Amount is 106, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₆

∴ If the Amount is 4929, then the Principal = ¹⁰⁰/₁₀₆ × 4929

= ^{100 × 4929}/₁₀₆

= ⁴⁹²⁹⁰⁰/₁₀₆

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(2) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 10% simple interest?

(3) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(6) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(9) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.