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) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.

(6) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.

(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 6% simple interest?

(9) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.