Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $8745

Rate of Simple Interest (R) = 2%

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

$8745 = P (1 + 2% × 5)

⇒ $8745 = P (1 + ²/₁₀₀ × 5)

⇒ $8745 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8745 = P (1 + ¹⁰/₁₀₀)

⇒ $8745 = P (^{100 + 10}/₁₀₀)

⇒ $8745 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8745

⇒ P = ⁸⁷⁴⁵/_¹¹⁰/100

⇒ P = 8745 × ¹⁰⁰/₁₁₀

⇒ P = ^{8745 × 100}/₁₁₀

⇒ P = ⁸⁷⁴⁵⁰⁰/₁₁₀

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8745, then the Principal = ¹⁰⁰/₁₁₀ × 8745

= ^{100 × 8745}/₁₁₀

= ⁸⁷⁴⁵⁰⁰/₁₁₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.

(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(5) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5995 to clear it?

(6) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?

(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(9) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.