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) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 8 years.

(2) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.

(3) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(6) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(8) Ashley had to pay $5232.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?

(10) In how much time a principal of $3150 will amount to $3339 at a simple interest of 2% per annum?