Simple Interest
Math MCQs

Question :    If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4300

Solution & Explanation

Solution

Given,

Amount (A) = $4988

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

$4988 = P (1 + 4% × 4)

⇒ $4988 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4988 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4988 = P (1 + ¹⁶/₁₀₀)

⇒ $4988 = P (^{100 + 16}/₁₀₀)

⇒ $4988 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4988

⇒ P = ⁴⁹⁸⁸/_¹¹⁶/100

⇒ P = 4988 × ¹⁰⁰/₁₁₆

⇒ P = ^{4988 × 100}/₁₁₆

⇒ P = ⁴⁹⁸⁸⁰⁰/₁₁₆

⇒ P = $4300

Thus, the sum borrowed (P) = $4300 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 4988, then the Principal = ¹⁰⁰/₁₁₆ × 4988

= ^{100 × 4988}/₁₁₆

= ⁴⁹⁸⁸⁰⁰/₁₁₆

= 4300

Thus, Principal = $4300

Thus, the sum borrowed = $4300 Answer

Similar Questions

(1) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 9% simple interest?

(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 4% simple interest for 3 years.

(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(6) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(7) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.

(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.