Simple Interest
Math MCQs

Question :    How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?

Correct Answer  $7400

Solution & Explanation

Solution

Given,

Amount (A) = $8880

Rate of Simple Interest (R) = 4%

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

$8880 = P (1 + 4% × 5)

⇒ $8880 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8880 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8880 = P (1 + ²⁰/₁₀₀)

⇒ $8880 = P (^{100 + 20}/₁₀₀)

⇒ $8880 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8880

⇒ P = ⁸⁸⁸⁰/_¹²⁰/100

⇒ P = 8880 × ¹⁰⁰/₁₂₀

⇒ P = ^{8880 × 100}/₁₂₀

⇒ P = ⁸⁸⁸⁰⁰⁰/₁₂₀

⇒ P = $7400

Thus, the sum borrowed (P) = $7400 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 8880, then the Principal = ¹⁰⁰/₁₂₀ × 8880

= ^{100 × 8880}/₁₂₀

= ⁸⁸⁸⁰⁰⁰/₁₂₀

= 7400

Thus, Principal = $7400

Thus, the sum borrowed = $7400 Answer

Similar Questions

(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?

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

(3) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 3% simple interest?

(4) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9387 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(8) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(10) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.