Simple Interest
Math MCQs

Question :    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) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.

(2) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?

(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.

(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 3 years.

(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.