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) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.

(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(3) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?

(6) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 3% simple interest?