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) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

(2) 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?

(3) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?

(5) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.

(6) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(7) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?

(9) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.