Simple Interest
Math MCQs

Question :    How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

Correct Answer  $7200

Solution & Explanation

Solution

Given,

Amount (A) = $8280

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

$8280 = P (1 + 3% × 5)

⇒ $8280 = P (1 + ³/₁₀₀ × 5)

⇒ $8280 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8280 = P (1 + ¹⁵/₁₀₀)

⇒ $8280 = P (^{100 + 15}/₁₀₀)

⇒ $8280 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8280

⇒ P = ⁸²⁸⁰/_¹¹⁵/100

⇒ P = 8280 × ¹⁰⁰/₁₁₅

⇒ P = ^{8280 × 100}/₁₁₅

⇒ P = ⁸²⁸⁰⁰⁰/₁₁₅

⇒ P = $7200

Thus, the sum borrowed (P) = $7200 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 8280, then the Principal = ¹⁰⁰/₁₁₅ × 8280

= ^{100 × 8280}/₁₁₅

= ⁸²⁸⁰⁰⁰/₁₁₅

= 7200

Thus, Principal = $7200

Thus, the sum borrowed = $7200 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.

(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.

(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 7 years.

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 3 years.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?