Simple Interest
Math MCQs

Question :    How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?

Correct Answer  $6600

Solution & Explanation

Solution

Given,

Amount (A) = $7920

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

$7920 = P (1 + 4% × 5)

⇒ $7920 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7920 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7920 = P (1 + ²⁰/₁₀₀)

⇒ $7920 = P (^{100 + 20}/₁₀₀)

⇒ $7920 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7920

⇒ P = ⁷⁹²⁰/_¹²⁰/100

⇒ P = 7920 × ¹⁰⁰/₁₂₀

⇒ P = ^{7920 × 100}/₁₂₀

⇒ P = ⁷⁹²⁰⁰⁰/₁₂₀

⇒ P = $6600

Thus, the sum borrowed (P) = $6600 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 7920, then the Principal = ¹⁰⁰/₁₂₀ × 7920

= ^{100 × 7920}/₁₂₀

= ⁷⁹²⁰⁰⁰/₁₂₀

= 6600

Thus, Principal = $6600

Thus, the sum borrowed = $6600 Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.

(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.

(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(8) How much loan did Deborah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8940 to clear it?

(9) 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.

(10) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.