Simple Interest
Math MCQs

Question :    How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?

Correct Answer  $5550

Solution & Explanation

Solution

Given,

Amount (A) = $6660

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

$6660 = P (1 + 4% × 5)

⇒ $6660 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6660 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6660 = P (1 + ²⁰/₁₀₀)

⇒ $6660 = P (^{100 + 20}/₁₀₀)

⇒ $6660 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6660

⇒ P = ⁶⁶⁶⁰/_¹²⁰/100

⇒ P = 6660 × ¹⁰⁰/₁₂₀

⇒ P = ^{6660 × 100}/₁₂₀

⇒ P = ⁶⁶⁶⁰⁰⁰/₁₂₀

⇒ P = $5550

Thus, the sum borrowed (P) = $5550 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 6660, then the Principal = ¹⁰⁰/₁₂₀ × 6660

= ^{100 × 6660}/₁₂₀

= ⁶⁶⁶⁰⁰⁰/₁₂₀

= 5550

Thus, Principal = $5550

Thus, the sum borrowed = $5550 Answer

Similar Questions

(1) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?

(2) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

(4) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8791 to clear the loan, then find the time period of the loan.

(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(8) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.