Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $6875

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

$6875 = P (1 + 2% × 5)

⇒ $6875 = P (1 + ²/₁₀₀ × 5)

⇒ $6875 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $6875 = P (1 + ¹⁰/₁₀₀)

⇒ $6875 = P (^{100 + 10}/₁₀₀)

⇒ $6875 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $6875

⇒ P = ⁶⁸⁷⁵/_¹¹⁰/100

⇒ P = 6875 × ¹⁰⁰/₁₁₀

⇒ P = ^{6875 × 100}/₁₁₀

⇒ P = ⁶⁸⁷⁵⁰⁰/₁₁₀

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 6875, then the Principal = ¹⁰⁰/₁₁₀ × 6875

= ^{100 × 6875}/₁₁₀

= ⁶⁸⁷⁵⁰⁰/₁₁₀

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) John had to pay $3392 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.

(4) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.

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

(8) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.

(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?