Simple Interest
Math MCQs

Question :    If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4814

Rate of Simple Interest (R) = 4%

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

$4814 = P (1 + 4% × 4)

⇒ $4814 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4814 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4814 = P (1 + ¹⁶/₁₀₀)

⇒ $4814 = P (^{100 + 16}/₁₀₀)

⇒ $4814 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4814

⇒ P = ⁴⁸¹⁴/_¹¹⁶/100

⇒ P = 4814 × ¹⁰⁰/₁₁₆

⇒ P = ^{4814 × 100}/₁₁₆

⇒ P = ⁴⁸¹⁴⁰⁰/₁₁₆

⇒ 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 4814, then the Principal = ¹⁰⁰/₁₁₆ × 4814

= ^{100 × 4814}/₁₁₆

= ⁴⁸¹⁴⁰⁰/₁₁₆

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(3) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?

(4) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.

(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.

(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 10% simple interest?