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) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

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

(4) Kimberly had to pay $5068.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?

(7) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 8 years.

(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(9) 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?

(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.