Simple Interest
Math MCQs

Question :    How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

Correct Answer  $6550

Solution & Explanation

Solution

Given,

Amount (A) = $7860

Rate of Simple Interest (R) = 4%

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

$7860 = P (1 + 4% × 5)

⇒ $7860 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7860 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7860 = P (1 + ²⁰/₁₀₀)

⇒ $7860 = P (^{100 + 20}/₁₀₀)

⇒ $7860 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7860

⇒ P = ⁷⁸⁶⁰/_¹²⁰/100

⇒ P = 7860 × ¹⁰⁰/₁₂₀

⇒ P = ^{7860 × 100}/₁₂₀

⇒ P = ⁷⁸⁶⁰⁰⁰/₁₂₀

⇒ P = $6550

Thus, the sum borrowed (P) = $6550 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 = 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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7860, then the Principal = ¹⁰⁰/₁₂₀ × 7860

= ^{100 × 7860}/₁₂₀

= ⁷⁸⁶⁰⁰⁰/₁₂₀

= 6550

Thus, Principal = $6550

Thus, the sum borrowed = $6550 Answer

Similar Questions

(1) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.

(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.

(5) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?

(7) How much loan did Kevin borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8520 to clear it?

(8) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.

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

(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 10% simple interest?