Simple Interest
Math MCQs

Question :    Emily had to pay $5462.5 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  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5462.5

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

$5462.5 = P (1 + 5% × 3)

⇒ $5462.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5462.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5462.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5462.5 = P (^{100 + 15}/₁₀₀)

⇒ $5462.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5462.5

⇒ P = ^5462.5/_¹¹⁵/100

⇒ P = 5462.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5462.5 × 100}/₁₁₅

⇒ P = ⁵⁴⁶²⁵⁰/₁₁₅

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5462.5, then the Principal = ¹⁰⁰/₁₁₅ × 5462.5

= ^{100 × 5462.5}/₁₁₅

= ⁵⁴⁶²⁵⁰/₁₁₅

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 7% simple interest.

(4) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 4% simple interest?

(7) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(10) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?