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) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(5) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.

(8) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(9) Jennifer had to pay $3542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) If Christopher paid $4480 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.