Simple Interest
Math MCQs

Question :    If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

Correct Answer  $4650

Solution & Explanation

Solution

Given,

Amount (A) = $5022

Rate of Simple Interest (R) = 2%

Time (T) = 4 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

$5022 = P (1 + 2% × 4)

⇒ $5022 = P (1 + ²/₁₀₀ × 4)

⇒ $5022 = P (1 + ^{2 × 4}/₁₀₀)

⇒ $5022 = P (1 + ⁸/₁₀₀)

⇒ $5022 = P (^{100 + 8}/₁₀₀)

⇒ $5022 = P × ¹⁰⁸/₁₀₀

⇒ P × ¹⁰⁸/₁₀₀ = $5022

⇒ P = ⁵⁰²²/_¹⁰⁸/100

⇒ P = 5022 × ¹⁰⁰/₁₀₈

⇒ P = ^{5022 × 100}/₁₀₈

⇒ P = ⁵⁰²²⁰⁰/₁₀₈

⇒ P = $4650

Thus, the sum borrowed (P) = $4650 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

Calculation of the Amount

Since, in the question, time = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 2 = 8

Thus, simple interest for 4 years = 8

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 8 = 108

Calculation of the Principal

Now,

∵ If the Amount is 108, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₀₈

∴ If the Amount is 5022, then the Principal = ¹⁰⁰/₁₀₈ × 5022

= ^{100 × 5022}/₁₀₈

= ⁵⁰²²⁰⁰/₁₀₈

= 4650

Thus, Principal = $4650

Thus, the sum borrowed = $4650 Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?

(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(3) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?

(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.

(5) How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?

(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.

(9) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.