Simple Interest
Math MCQs

Question :  ( 1 of 10 )  How much loan did Stephanie borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9060 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $9060

Rate of Simple Interest (R) = 4%

Time (T) = 5 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

$9060 = P (1 + 4% × 5)

⇒ $9060 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9060 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9060 = P (1 + ²⁰/₁₀₀)

⇒ $9060 = P (^{100 + 20}/₁₀₀)

⇒ $9060 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9060

⇒ P = ⁹⁰⁶⁰/_¹²⁰/100

⇒ P = 9060 × ¹⁰⁰/₁₂₀

⇒ P = ^{9060 × 100}/₁₂₀

⇒ P = ⁹⁰⁶⁰⁰⁰/₁₂₀

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9060, then the Principal = ¹⁰⁰/₁₂₀ × 9060

= ^{100 × 9060}/₁₂₀

= ⁹⁰⁶⁰⁰⁰/₁₂₀

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?

(2) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(5) How much loan did Mary borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5555 to clear it?

(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.

(9) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.