Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $7980

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

$7980 = P (1 + 4% × 5)

⇒ $7980 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7980 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7980 = P (1 + ²⁰/₁₀₀)

⇒ $7980 = P (^{100 + 20}/₁₀₀)

⇒ $7980 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7980

⇒ P = ⁷⁹⁸⁰/_¹²⁰/100

⇒ P = 7980 × ¹⁰⁰/₁₂₀

⇒ P = ^{7980 × 100}/₁₂₀

⇒ P = ⁷⁹⁸⁰⁰⁰/₁₂₀

⇒ P = $6650

Thus, the sum borrowed (P) = $6650 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 7980, then the Principal = ¹⁰⁰/₁₂₀ × 7980

= ^{100 × 7980}/₁₂₀

= ⁷⁹⁸⁰⁰⁰/₁₂₀

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(2) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.

(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(10) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.