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) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.

(3) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 7 years.

(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(7) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(8) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 6% simple interest?