Simple Interest
Math MCQs

Question :    How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

Correct Answer  $7650

Solution & Explanation

Solution

Given,

Amount (A) = $8415

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

$8415 = P (1 + 2% × 5)

⇒ $8415 = P (1 + ²/₁₀₀ × 5)

⇒ $8415 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8415 = P (1 + ¹⁰/₁₀₀)

⇒ $8415 = P (^{100 + 10}/₁₀₀)

⇒ $8415 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8415

⇒ P = ⁸⁴¹⁵/_¹¹⁰/100

⇒ P = 8415 × ¹⁰⁰/₁₁₀

⇒ P = ^{8415 × 100}/₁₁₀

⇒ P = ⁸⁴¹⁵⁰⁰/₁₁₀

⇒ P = $7650

Thus, the sum borrowed (P) = $7650 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 8415, then the Principal = ¹⁰⁰/₁₁₀ × 8415

= ^{100 × 8415}/₁₁₀

= ⁸⁴¹⁵⁰⁰/₁₁₀

= 7650

Thus, Principal = $7650

Thus, the sum borrowed = $7650 Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

(4) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 4 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 3% simple interest for 3 years.

(8) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.

(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?