Simple Interest
Math MCQs

Question :    How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

Correct Answer  $7450

Solution & Explanation

Solution

Given,

Amount (A) = $8567.5

Rate of Simple Interest (R) = 3%

Time (T) = 5 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

$8567.5 = P (1 + 3% × 5)

⇒ $8567.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8567.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8567.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8567.5 = P (^{100 + 15}/₁₀₀)

⇒ $8567.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8567.5

⇒ P = ^8567.5/_¹¹⁵/100

⇒ P = 8567.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8567.5 × 100}/₁₁₅

⇒ P = ⁸⁵⁶⁷⁵⁰/₁₁₅

⇒ P = $7450

Thus, the sum borrowed (P) = $7450 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 8567.5, then the Principal = ¹⁰⁰/₁₁₅ × 8567.5

= ^{100 × 8567.5}/₁₁₅

= ⁸⁵⁶⁷⁵⁰/₁₁₅

= 7450

Thus, Principal = $7450

Thus, the sum borrowed = $7450 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.

(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?

(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.

(10) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.