Simple Interest
Math MCQs

Question :    If Nancy paid $4980 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $4150

Solution & Explanation

Solution

Given,

Amount (A) = $4980

Rate of Simple Interest (R) = 5%

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

$4980 = P (1 + 5% × 4)

⇒ $4980 = P (1 + ⁵/₁₀₀ × 4)

⇒ $4980 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $4980 = P (1 + ²⁰/₁₀₀)

⇒ $4980 = P (^{100 + 20}/₁₀₀)

⇒ $4980 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $4980

⇒ P = ⁴⁹⁸⁰/_¹²⁰/100

⇒ P = 4980 × ¹⁰⁰/₁₂₀

⇒ P = ^{4980 × 100}/₁₂₀

⇒ P = ⁴⁹⁸⁰⁰⁰/₁₂₀

⇒ 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 = 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 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 4980, then the Principal = ¹⁰⁰/₁₂₀ × 4980

= ^{100 × 4980}/₁₂₀

= ⁴⁹⁸⁰⁰⁰/₁₂₀

= 4150

Thus, Principal = $4150

Thus, the sum borrowed = $4150 Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(2) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.

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

(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?

(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

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

(9) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.