Simple Interest
Math MCQs

Question :    Donna had to pay $5432 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  $4850

Solution & Explanation

Solution

Given,

Amount (A) = $5432

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

$5432 = P (1 + 4% × 3)

⇒ $5432 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5432 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5432 = P (1 + ¹²/₁₀₀)

⇒ $5432 = P (^{100 + 12}/₁₀₀)

⇒ $5432 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5432

⇒ P = ⁵⁴³²/_¹¹²/100

⇒ P = 5432 × ¹⁰⁰/₁₁₂

⇒ P = ^{5432 × 100}/₁₁₂

⇒ P = ⁵⁴³²⁰⁰/₁₁₂

⇒ P = $4850

Thus, the sum borrowed (P) = $4850 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 5432, then the Principal = ¹⁰⁰/₁₁₂ × 5432

= ^{100 × 5432}/₁₁₂

= ⁵⁴³²⁰⁰/₁₁₂

= 4850

Thus, Principal = $4850

Thus, the sum borrowed = $4850 Answer

Similar Questions

(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(2) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(4) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.

(6) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 8 years.

(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

(10) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.