Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $7647.5

Rate of Simple Interest (R) = 3%

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

$7647.5 = P (1 + 3% × 5)

⇒ $7647.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7647.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7647.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7647.5 = P (^{100 + 15}/₁₀₀)

⇒ $7647.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7647.5

⇒ P = ^7647.5/_¹¹⁵/100

⇒ P = 7647.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7647.5 × 100}/₁₁₅

⇒ P = ⁷⁶⁴⁷⁵⁰/₁₁₅

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 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 7647.5, then the Principal = ¹⁰⁰/₁₁₅ × 7647.5

= ^{100 × 7647.5}/₁₁₅

= ⁷⁶⁴⁷⁵⁰/₁₁₅

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.

(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

(3) 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.

(4) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.

(5) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.