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) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?

(4) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?

(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.

(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.

(9) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?

(10) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?