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) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 7% simple interest?

(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

(5) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.

(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.

(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.