Simple Interest
Math MCQs

Question :    How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

Correct Answer  $7600

Solution & Explanation

Solution

Given,

Amount (A) = $8740

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

$8740 = P (1 + 3% × 5)

⇒ $8740 = P (1 + ³/₁₀₀ × 5)

⇒ $8740 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8740 = P (1 + ¹⁵/₁₀₀)

⇒ $8740 = P (^{100 + 15}/₁₀₀)

⇒ $8740 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8740

⇒ P = ⁸⁷⁴⁰/_¹¹⁵/100

⇒ P = 8740 × ¹⁰⁰/₁₁₅

⇒ P = ^{8740 × 100}/₁₁₅

⇒ P = ⁸⁷⁴⁰⁰⁰/₁₁₅

⇒ 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 = 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 8740, then the Principal = ¹⁰⁰/₁₁₅ × 8740

= ^{100 × 8740}/₁₁₅

= ⁸⁷⁴⁰⁰⁰/₁₁₅

= 7600

Thus, Principal = $7600

Thus, the sum borrowed = $7600 Answer

Similar Questions

(1) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 6% simple interest?

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

(3) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(5) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(6) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?

(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?

(8) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?

(9) David had to pay $3706 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.