Simple Interest
Math MCQs

Question :    How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?

Correct Answer  $5250

Solution & Explanation

Solution

Given,

Amount (A) = $6037.5

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

$6037.5 = P (1 + 3% × 5)

⇒ $6037.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6037.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6037.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6037.5 = P (^{100 + 15}/₁₀₀)

⇒ $6037.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6037.5

⇒ P = ^6037.5/_¹¹⁵/100

⇒ P = 6037.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6037.5 × 100}/₁₁₅

⇒ P = ⁶⁰³⁷⁵⁰/₁₁₅

⇒ P = $5250

Thus, the sum borrowed (P) = $5250 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 6037.5, then the Principal = ¹⁰⁰/₁₁₅ × 6037.5

= ^{100 × 6037.5}/₁₁₅

= ⁶⁰³⁷⁵⁰/₁₁₅

= 5250

Thus, Principal = $5250

Thus, the sum borrowed = $5250 Answer

Similar Questions

(1) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.

(3) If Thomas paid $4104 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 4% simple interest.

(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(7) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 3 years.

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.