Simple Interest
Math MCQs

Question :    How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

Correct Answer  $6850

Solution & Explanation

Solution

Given,

Amount (A) = $8562.5

Rate of Simple Interest (R) = 5%

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

$8562.5 = P (1 + 5% × 5)

⇒ $8562.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8562.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8562.5 = P (1 + ²⁵/₁₀₀)

⇒ $8562.5 = P (^{100 + 25}/₁₀₀)

⇒ $8562.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8562.5

⇒ P = ^8562.5/_¹²⁵/100

⇒ P = 8562.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8562.5 × 100}/₁₂₅

⇒ P = ⁸⁵⁶²⁵⁰/₁₂₅

⇒ P = $6850

Thus, the sum borrowed (P) = $6850 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8562.5, then the Principal = ¹⁰⁰/₁₂₅ × 8562.5

= ^{100 × 8562.5}/₁₂₅

= ⁸⁵⁶²⁵⁰/₁₂₅

= 6850

Thus, Principal = $6850

Thus, the sum borrowed = $6850 Answer

Similar Questions

(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(2) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

(5) Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 7 years.

(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.

(9) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

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