Simple Interest
Math MCQs

Question :    Emily had to pay $5177.5 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5177.5

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

$5177.5 = P (1 + 3% × 3)

⇒ $5177.5 = P (1 + ³/₁₀₀ × 3)

⇒ $5177.5 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5177.5 = P (1 + ⁹/₁₀₀)

⇒ $5177.5 = P (^{100 + 9}/₁₀₀)

⇒ $5177.5 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5177.5

⇒ P = ^5177.5/_¹⁰⁹/100

⇒ P = 5177.5 × ¹⁰⁰/₁₀₉

⇒ P = ^{5177.5 × 100}/₁₀₉

⇒ P = ⁵¹⁷⁷⁵⁰/₁₀₉

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5177.5, then the Principal = ¹⁰⁰/₁₀₉ × 5177.5

= ^{100 × 5177.5}/₁₀₉

= ⁵¹⁷⁷⁵⁰/₁₀₉

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 10% simple interest?

(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(5) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?

(6) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.

(7) If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 7% simple interest?

(10) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?