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) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.

(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(4) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?

(6) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?

(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(9) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.