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) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $9291 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.

(4) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.

(8) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.