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) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(2) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(3) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(5) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 10% simple interest?

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(7) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 9% simple interest?

(8) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.

(9) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.