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) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(2) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.

(3) If Betty paid $5100 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.

(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.

(6) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.

(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.

(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.