Simple Interest
Math MCQs

Question :    Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

Correct Answer  $4500

Solution & Explanation

Solution

Given,

Amount (A) = $5040

Rate of Simple Interest (R) = 4%

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

$5040 = P (1 + 4% × 3)

⇒ $5040 = P (1 + ⁴/₁₀₀ × 3)

⇒ $5040 = P (1 + ^{4 × 3}/₁₀₀)

⇒ $5040 = P (1 + ¹²/₁₀₀)

⇒ $5040 = P (^{100 + 12}/₁₀₀)

⇒ $5040 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5040

⇒ P = ⁵⁰⁴⁰/_¹¹²/100

⇒ P = 5040 × ¹⁰⁰/₁₁₂

⇒ P = ^{5040 × 100}/₁₁₂

⇒ P = ⁵⁰⁴⁰⁰⁰/₁₁₂

⇒ P = $4500

Thus, the sum borrowed (P) = $4500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 12

Thus, simple interest for 3 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5040, then the Principal = ¹⁰⁰/₁₁₂ × 5040

= ^{100 × 5040}/₁₁₂

= ⁵⁰⁴⁰⁰⁰/₁₁₂

= 4500

Thus, Principal = $4500

Thus, the sum borrowed = $4500 Answer

Similar Questions

(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?

(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(3) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(6) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

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

(9) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 9% simple interest?