Simple Interest
Math MCQs

Question :    How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $8682.5

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

$8682.5 = P (1 + 3% × 5)

⇒ $8682.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8682.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8682.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8682.5 = P (^{100 + 15}/₁₀₀)

⇒ $8682.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8682.5

⇒ P = ^8682.5/_¹¹⁵/100

⇒ P = 8682.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8682.5 × 100}/₁₁₅

⇒ P = ⁸⁶⁸²⁵⁰/₁₁₅

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 8682.5, then the Principal = ¹⁰⁰/₁₁₅ × 8682.5

= ^{100 × 8682.5}/₁₁₅

= ⁸⁶⁸²⁵⁰/₁₁₅

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?

(2) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(3) 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.

(4) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?

(6) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(9) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.