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) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(3) Charles had to pay $4368 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(4) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(6) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(10) In how much time a principal of $3100 will amount to $3875 at a simple interest of 5% per annum?