Simple Interest
Math MCQs

Question :    Steven had to pay $5014 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  $4600

Solution & Explanation

Solution

Given,

Amount (A) = $5014

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

$5014 = P (1 + 3% × 3)

⇒ $5014 = P (1 + ³/₁₀₀ × 3)

⇒ $5014 = P (1 + ^{3 × 3}/₁₀₀)

⇒ $5014 = P (1 + ⁹/₁₀₀)

⇒ $5014 = P (^{100 + 9}/₁₀₀)

⇒ $5014 = P × ¹⁰⁹/₁₀₀

⇒ P × ¹⁰⁹/₁₀₀ = $5014

⇒ P = ⁵⁰¹⁴/_¹⁰⁹/100

⇒ P = 5014 × ¹⁰⁰/₁₀₉

⇒ P = ^{5014 × 100}/₁₀₉

⇒ P = ⁵⁰¹⁴⁰⁰/₁₀₉

⇒ P = $4600

Thus, the sum borrowed (P) = $4600 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 5014, then the Principal = ¹⁰⁰/₁₀₉ × 5014

= ^{100 × 5014}/₁₀₉

= ⁵⁰¹⁴⁰⁰/₁₀₉

= 4600

Thus, Principal = $4600

Thus, the sum borrowed = $4600 Answer

Similar Questions

(1) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(7) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?

(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.