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 if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(2) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10064 to clear the loan, then find the time period of the loan.

(3) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.

(6) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.

(9) Kimberly had to pay $5208 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.