Simple Interest
Math MCQs

Question :    If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4648

Rate of Simple Interest (R) = 3%

Time (T) = 4 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

$4648 = P (1 + 3% × 4)

⇒ $4648 = P (1 + ³/₁₀₀ × 4)

⇒ $4648 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $4648 = P (1 + ¹²/₁₀₀)

⇒ $4648 = P (^{100 + 12}/₁₀₀)

⇒ $4648 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $4648

⇒ P = ⁴⁶⁴⁸/_¹¹²/100

⇒ P = 4648 × ¹⁰⁰/₁₁₂

⇒ P = ^{4648 × 100}/₁₁₂

⇒ P = ⁴⁶⁴⁸⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 4648, then the Principal = ¹⁰⁰/₁₁₂ × 4648

= ^{100 × 4648}/₁₁₂

= ⁴⁶⁴⁸⁰⁰/₁₁₂

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?

(4) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?

(5) How much loan did Daniel borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7015 to clear it?

(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.