Simple Interest
Math MCQs

Question :    If Kenneth paid $5800 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $5000

Solution & Explanation

Solution

Given,

Amount (A) = $5800

Rate of Simple Interest (R) = 4%

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

$5800 = P (1 + 4% × 4)

⇒ $5800 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5800 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5800 = P (1 + ¹⁶/₁₀₀)

⇒ $5800 = P (^{100 + 16}/₁₀₀)

⇒ $5800 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5800

⇒ P = ⁵⁸⁰⁰/_¹¹⁶/100

⇒ P = 5800 × ¹⁰⁰/₁₁₆

⇒ P = ^{5800 × 100}/₁₁₆

⇒ P = ⁵⁸⁰⁰⁰⁰/₁₁₆

⇒ P = $5000

Thus, the sum borrowed (P) = $5000 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 = 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 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5800, then the Principal = ¹⁰⁰/₁₁₆ × 5800

= ^{100 × 5800}/₁₁₆

= ⁵⁸⁰⁰⁰⁰/₁₁₆

= 5000

Thus, Principal = $5000

Thus, the sum borrowed = $5000 Answer

Similar Questions

(1) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?

(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?

(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7208 to clear the loan, then find the time period of the loan.

(6) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 7% simple interest?

(7) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?

(9) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?