Simple Interest
Math MCQs

Question :    How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $9437.5

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

$9437.5 = P (1 + 5% × 5)

⇒ $9437.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9437.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9437.5 = P (1 + ²⁵/₁₀₀)

⇒ $9437.5 = P (^{100 + 25}/₁₀₀)

⇒ $9437.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9437.5

⇒ P = ^9437.5/_¹²⁵/100

⇒ P = 9437.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{9437.5 × 100}/₁₂₅

⇒ P = ⁹⁴³⁷⁵⁰/₁₂₅

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 9437.5, then the Principal = ¹⁰⁰/₁₂₅ × 9437.5

= ^{100 × 9437.5}/₁₂₅

= ⁹⁴³⁷⁵⁰/₁₂₅

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(4) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(6) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(7) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(8) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(9) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.