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) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

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

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?

(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?

(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(7) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 4 years.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.