Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $9180

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

$9180 = P (1 + 4% × 5)

⇒ $9180 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9180 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9180 = P (1 + ²⁰/₁₀₀)

⇒ $9180 = P (^{100 + 20}/₁₀₀)

⇒ $9180 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9180

⇒ P = ⁹¹⁸⁰/_¹²⁰/100

⇒ P = 9180 × ¹⁰⁰/₁₂₀

⇒ P = ^{9180 × 100}/₁₂₀

⇒ P = ⁹¹⁸⁰⁰⁰/₁₂₀

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 9180, then the Principal = ¹⁰⁰/₁₂₀ × 9180

= ^{100 × 9180}/₁₂₀

= ⁹¹⁸⁰⁰⁰/₁₂₀

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $7952 to clear the loan, then find the time period of the loan.

(2) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.

(5) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Jennifer had to pay $3640 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.

(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.