Simple Interest
Math MCQs

Question :    How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?

Correct Answer  $6350

Solution & Explanation

Solution

Given,

Amount (A) = $7937.5

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

$7937.5 = P (1 + 5% × 5)

⇒ $7937.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7937.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7937.5 = P (1 + ²⁵/₁₀₀)

⇒ $7937.5 = P (^{100 + 25}/₁₀₀)

⇒ $7937.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7937.5

⇒ P = ^7937.5/_¹²⁵/100

⇒ P = 7937.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7937.5 × 100}/₁₂₅

⇒ P = ⁷⁹³⁷⁵⁰/₁₂₅

⇒ P = $6350

Thus, the sum borrowed (P) = $6350 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 7937.5, then the Principal = ¹⁰⁰/₁₂₅ × 7937.5

= ^{100 × 7937.5}/₁₂₅

= ⁷⁹³⁷⁵⁰/₁₂₅

= 6350

Thus, Principal = $6350

Thus, the sum borrowed = $6350 Answer

Similar Questions

(1) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(2) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?

(8) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(9) If Donna paid $5820 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.