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) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 7% simple interest?

(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

(3) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(4) What amount does John have to pay after 5 years if he takes a loan of $3200 at 4% simple interest?

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(6) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.

(9) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.