Simple Interest
Math MCQs

Question :    How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

Correct Answer  $6900

Solution & Explanation

Solution

Given,

Amount (A) = $8280

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

$8280 = P (1 + 4% × 5)

⇒ $8280 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8280 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8280 = P (1 + ²⁰/₁₀₀)

⇒ $8280 = P (^{100 + 20}/₁₀₀)

⇒ $8280 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8280

⇒ P = ⁸²⁸⁰/_¹²⁰/100

⇒ P = 8280 × ¹⁰⁰/₁₂₀

⇒ P = ^{8280 × 100}/₁₂₀

⇒ P = ⁸²⁸⁰⁰⁰/₁₂₀

⇒ P = $6900

Thus, the sum borrowed (P) = $6900 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 8280, then the Principal = ¹⁰⁰/₁₂₀ × 8280

= ^{100 × 8280}/₁₂₀

= ⁸²⁸⁰⁰⁰/₁₂₀

= 6900

Thus, Principal = $6900

Thus, the sum borrowed = $6900 Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

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

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?

(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?

(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.

(6) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 4% simple interest?

(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?

(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(10) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.