Simple Interest
Math MCQs

Question :    Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

Correct Answer  $4200

Solution & Explanation

Solution

Given,

Amount (A) = $4578

Rate of Simple Interest (R) = 3%

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

$4578 = P (1 + 3% × 3)

⇒ $4578 = P (1 + ³/₁₀₀ × 3)

⇒ $4578 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4578 = P (1 + ⁹/₁₀₀)

⇒ $4578 = P (^{100 + 9}/₁₀₀)

⇒ $4578 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4578

⇒ P = ⁴⁵⁷⁸/_¹⁰⁹/100

⇒ P = 4578 × ¹⁰⁰/₁₀₉

⇒ P = ^{4578 × 100}/₁₀₉

⇒ P = ⁴⁵⁷⁸⁰⁰/₁₀₉

⇒ P = $4200

Thus, the sum borrowed (P) = $4200 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 9

Thus, simple interest for 3 years = 9

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 9 = 109

Calculation of the Principal

Now,

∵ If the Amount is 109, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₉

∴ If the Amount is 4578, then the Principal = ¹⁰⁰/₁₀₉ × 4578

= ^{100 × 4578}/₁₀₉

= ⁴⁵⁷⁸⁰⁰/₁₀₉

= 4200

Thus, Principal = $4200

Thus, the sum borrowed = $4200 Answer

Similar Questions

(1) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.

(4) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(7) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 3% simple interest?

(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(10) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.