Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9500 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $9500

Rate of Simple Interest (R) = 5%

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

$9500 = P (1 + 5% × 5)

⇒ $9500 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9500 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9500 = P (1 + ²⁵/₁₀₀)

⇒ $9500 = P (^{100 + 25}/₁₀₀)

⇒ $9500 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9500

⇒ P = ⁹⁵⁰⁰/_¹²⁵/100

⇒ P = 9500 × ¹⁰⁰/₁₂₅

⇒ P = ^{9500 × 100}/₁₂₅

⇒ P = ⁹⁵⁰⁰⁰⁰/₁₂₅

⇒ P = $7600

Thus, the sum borrowed (P) = $7600 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 9500, then the Principal = ¹⁰⁰/₁₂₅ × 9500

= ^{100 × 9500}/₁₂₅

= ⁹⁵⁰⁰⁰⁰/₁₂₅

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(2) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(6) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(7) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(10) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.