Simple Interest
Math MCQs

Question :    Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4082.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4082.5 = P (1 + 5% × 3)

⇒ $4082.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4082.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4082.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4082.5 = P (^{100 + 15}/₁₀₀)

⇒ $4082.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4082.5

⇒ P = ^4082.5/_¹¹⁵/100

⇒ P = 4082.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4082.5 × 100}/₁₁₅

⇒ P = ⁴⁰⁸²⁵⁰/₁₁₅

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 4082.5, then the Principal = ¹⁰⁰/₁₁₅ × 4082.5

= ^{100 × 4082.5}/₁₁₅

= ⁴⁰⁸²⁵⁰/₁₁₅

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(3) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(4) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.

(5) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.

(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.

(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 8% simple interest?

(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.