Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9937.5 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9937.5

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

$9937.5 = P (1 + 5% × 5)

⇒ $9937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9937.5 = P (1 + ²⁵/₁₀₀)

⇒ $9937.5 = P (^{100 + 25}/₁₀₀)

⇒ $9937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9937.5

⇒ P = ^9937.5/_¹²⁵/100

⇒ P = 9937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9937.5 × 100}/₁₂₅

⇒ P = ⁹⁹³⁷⁵⁰/₁₂₅

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 9937.5, then the Principal = ¹⁰⁰/₁₂₅ × 9937.5

= ^{100 × 9937.5}/₁₂₅

= ⁹⁹³⁷⁵⁰/₁₂₅

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?

(5) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.

(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(8) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.