Simple Interest
Math MCQs

Question :    If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4250

Solution & Explanation

Solution

Given,

Amount (A) = $4930

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

$4930 = P (1 + 4% × 4)

⇒ $4930 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4930 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4930 = P (1 + ¹⁶/₁₀₀)

⇒ $4930 = P (^{100 + 16}/₁₀₀)

⇒ $4930 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4930

⇒ P = ⁴⁹³⁰/_¹¹⁶/100

⇒ P = 4930 × ¹⁰⁰/₁₁₆

⇒ P = ^{4930 × 100}/₁₁₆

⇒ P = ⁴⁹³⁰⁰⁰/₁₁₆

⇒ P = $4250

Thus, the sum borrowed (P) = $4250 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 4930, then the Principal = ¹⁰⁰/₁₁₆ × 4930

= ^{100 × 4930}/₁₁₆

= ⁴⁹³⁰⁰⁰/₁₁₆

= 4250

Thus, Principal = $4250

Thus, the sum borrowed = $4250 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

(2) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(5) Donna had to pay $5432 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.

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