Simple Interest
Math MCQs

Question :    Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $4550

Solution & Explanation

Solution

Given,

Amount (A) = $5232.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$5232.5 = P (1 + 5% × 3)

⇒ $5232.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5232.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5232.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5232.5 = P (^{100 + 15}/₁₀₀)

⇒ $5232.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5232.5

⇒ P = ^5232.5/_¹¹⁵/100

⇒ P = 5232.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5232.5 × 100}/₁₁₅

⇒ P = ⁵²³²⁵⁰/₁₁₅

⇒ P = $4550

Thus, the sum borrowed (P) = $4550 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 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 5232.5, then the Principal = ¹⁰⁰/₁₁₅ × 5232.5

= ^{100 × 5232.5}/₁₁₅

= ⁵²³²⁵⁰/₁₁₅

= 4550

Thus, Principal = $4550

Thus, the sum borrowed = $4550 Answer

Similar Questions

(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(2) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 3 years.

(3) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.

(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(5) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?

(6) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.

(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 9% simple interest?

(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?

(9) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.