Simple Interest
Math MCQs

Question :    Nancy had to pay $4772.5 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  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4772.5

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

$4772.5 = P (1 + 5% × 3)

⇒ $4772.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4772.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4772.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4772.5 = P (^{100 + 15}/₁₀₀)

⇒ $4772.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4772.5

⇒ P = ^4772.5/_¹¹⁵/100

⇒ P = 4772.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4772.5 × 100}/₁₁₅

⇒ P = ⁴⁷⁷²⁵⁰/₁₁₅

⇒ P = $4150

Thus, the sum borrowed (P) = $4150 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 4772.5, then the Principal = ¹⁰⁰/₁₁₅ × 4772.5

= ^{100 × 4772.5}/₁₁₅

= ⁴⁷⁷²⁵⁰/₁₁₅

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.

(4) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(5) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?

(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(7) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 7 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.