Simple Interest
Math MCQs

Question :    How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?

Correct Answer  $7150

Solution & Explanation

Solution

Given,

Amount (A) = $8222.5

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

$8222.5 = P (1 + 3% × 5)

⇒ $8222.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8222.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8222.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8222.5 = P (^{100 + 15}/₁₀₀)

⇒ $8222.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8222.5

⇒ P = ^8222.5/_¹¹⁵/100

⇒ P = 8222.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8222.5 × 100}/₁₁₅

⇒ P = ⁸²²²⁵⁰/₁₁₅

⇒ P = $7150

Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = ¹⁰⁰/₁₁₅ × 8222.5

= ^{100 × 8222.5}/₁₁₅

= ⁸²²²⁵⁰/₁₁₅

= 7150

Thus, Principal = $7150

Thus, the sum borrowed = $7150 Answer

Similar Questions

(1) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?

(3) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(5) If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 7 years.

(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 6% 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.