Simple Interest
Math MCQs

Question :    Anthony had to pay $4687 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  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4687

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

$4687 = P (1 + 3% × 3)

⇒ $4687 = P (1 + ³/₁₀₀ × 3)

⇒ $4687 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $4687 = P (1 + ⁹/₁₀₀)

⇒ $4687 = P (^{100 + 9}/₁₀₀)

⇒ $4687 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $4687

⇒ P = ⁴⁶⁸⁷/_¹⁰⁹/100

⇒ P = 4687 × ¹⁰⁰/₁₀₉

⇒ P = ^{4687 × 100}/₁₀₉

⇒ P = ⁴⁶⁸⁷⁰⁰/₁₀₉

⇒ 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 = 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 4687, then the Principal = ¹⁰⁰/₁₀₉ × 4687

= ^{100 × 4687}/₁₀₉

= ⁴⁶⁸⁷⁰⁰/₁₀₉

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?

(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

(3) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 9% simple interest?

(7) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.

(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(10) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.