Simple Interest
Math MCQs

Question :    Anthony had to pay $4558 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  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4558

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

$4558 = P (1 + 2% × 3)

⇒ $4558 = P (1 + ²/₁₀₀ × 3)

⇒ $4558 = P (1 + ^{2 × 3}/₁₀₀)

⇒ $4558 = P (1 + ⁶/₁₀₀)

⇒ $4558 = P (^{100 + 6}/₁₀₀)

⇒ $4558 = P × ¹⁰⁶/₁₀₀

⇒ P × ¹⁰⁶/₁₀₀ = $4558

⇒ P = ⁴⁵⁵⁸/_¹⁰⁶/100

⇒ P = 4558 × ¹⁰⁰/₁₀₆

⇒ P = ^{4558 × 100}/₁₀₆

⇒ P = ⁴⁵⁵⁸⁰⁰/₁₀₆

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4558, then the Principal = ¹⁰⁰/₁₀₆ × 4558

= ^{100 × 4558}/₁₀₆

= ⁴⁵⁵⁸⁰⁰/₁₀₆

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?

(3) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 4 years.

(4) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(6) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.

(7) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(9) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(10) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.