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) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(2) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.

(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.

(4) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(6) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.

(9) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.