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

(2) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?

(3) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 3 years.

(6) How much loan did Robert borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6120 to clear it?

(7) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

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

(9) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 4 years.

(10) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.