Simple Interest
Math MCQs

Question :    Sandra had to pay $5117.5 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  $4450

Solution & Explanation

Solution

Given,

Amount (A) = $5117.5

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

$5117.5 = P (1 + 5% × 3)

⇒ $5117.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $5117.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $5117.5 = P (1 + ¹⁵/₁₀₀)

⇒ $5117.5 = P (^{100 + 15}/₁₀₀)

⇒ $5117.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $5117.5

⇒ P = ^5117.5/_¹¹⁵/100

⇒ P = 5117.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{5117.5 × 100}/₁₁₅

⇒ P = ⁵¹¹⁷⁵⁰/₁₁₅

⇒ P = $4450

Thus, the sum borrowed (P) = $4450 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 5117.5, then the Principal = ¹⁰⁰/₁₁₅ × 5117.5

= ^{100 × 5117.5}/₁₁₅

= ⁵¹¹⁷⁵⁰/₁₁₅

= 4450

Thus, Principal = $4450

Thus, the sum borrowed = $4450 Answer

Similar Questions

(1) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?

(3) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(4) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.

(7) 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.

(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8940 to clear the loan, then find the time period of the loan.

(9) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(10) What amount will be due after 2 years if David borrowed a sum of $3200 at a 8% simple interest?