Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7820 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $7820

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

$7820 = P (1 + 3% × 5)

⇒ $7820 = P (1 + ³/₁₀₀ × 5)

⇒ $7820 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7820 = P (1 + ¹⁵/₁₀₀)

⇒ $7820 = P (^{100 + 15}/₁₀₀)

⇒ $7820 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7820

⇒ P = ⁷⁸²⁰/_¹¹⁵/100

⇒ P = 7820 × ¹⁰⁰/₁₁₅

⇒ P = ^{7820 × 100}/₁₁₅

⇒ P = ⁷⁸²⁰⁰⁰/₁₁₅

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 7820, then the Principal = ¹⁰⁰/₁₁₅ × 7820

= ^{100 × 7820}/₁₁₅

= ⁷⁸²⁰⁰⁰/₁₁₅

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.

(2) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(3) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.

(7) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.

(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(9) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.