Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $8745

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

$8745 = P (1 + 2% × 5)

⇒ $8745 = P (1 + ²/₁₀₀ × 5)

⇒ $8745 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8745 = P (1 + ¹⁰/₁₀₀)

⇒ $8745 = P (^{100 + 10}/₁₀₀)

⇒ $8745 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8745

⇒ P = ⁸⁷⁴⁵/_¹¹⁰/100

⇒ P = 8745 × ¹⁰⁰/₁₁₀

⇒ P = ^{8745 × 100}/₁₁₀

⇒ P = ⁸⁷⁴⁵⁰⁰/₁₁₀

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 8745, then the Principal = ¹⁰⁰/₁₁₀ × 8745

= ^{100 × 8745}/₁₁₀

= ⁸⁷⁴⁵⁰⁰/₁₁₀

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.

(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 7% simple interest?

(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 4 years.

(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.

(5) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(7) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(9) How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.