Simple Interest
Math MCQs

Question :    How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

Correct Answer  $6650

Solution & Explanation

Solution

Given,

Amount (A) = $7315

Rate of Simple Interest (R) = 2%

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

$7315 = P (1 + 2% × 5)

⇒ $7315 = P (1 + ²/₁₀₀ × 5)

⇒ $7315 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $7315 = P (1 + ¹⁰/₁₀₀)

⇒ $7315 = P (^{100 + 10}/₁₀₀)

⇒ $7315 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $7315

⇒ P = ⁷³¹⁵/_¹¹⁰/100

⇒ P = 7315 × ¹⁰⁰/₁₁₀

⇒ P = ^{7315 × 100}/₁₁₀

⇒ P = ⁷³¹⁵⁰⁰/₁₁₀

⇒ 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 = 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 = 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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 7315, then the Principal = ¹⁰⁰/₁₁₀ × 7315

= ^{100 × 7315}/₁₁₀

= ⁷³¹⁵⁰⁰/₁₁₀

= 6650

Thus, Principal = $6650

Thus, the sum borrowed = $6650 Answer

Similar Questions

(1) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(3) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?

(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?

(6) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?

(7) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?

(9) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.