Simple Interest
Math MCQs

Question :    How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?

Correct Answer  $5700

Solution & Explanation

Solution

Given,

Amount (A) = $6840

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

$6840 = P (1 + 4% × 5)

⇒ $6840 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6840 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6840 = P (1 + ²⁰/₁₀₀)

⇒ $6840 = P (^{100 + 20}/₁₀₀)

⇒ $6840 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6840

⇒ P = ⁶⁸⁴⁰/_¹²⁰/100

⇒ P = 6840 × ¹⁰⁰/₁₂₀

⇒ P = ^{6840 × 100}/₁₂₀

⇒ P = ⁶⁸⁴⁰⁰⁰/₁₂₀

⇒ P = $5700

Thus, the sum borrowed (P) = $5700 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 6840, then the Principal = ¹⁰⁰/₁₂₀ × 6840

= ^{100 × 6840}/₁₂₀

= ⁶⁸⁴⁰⁰⁰/₁₂₀

= 5700

Thus, Principal = $5700

Thus, the sum borrowed = $5700 Answer

Similar Questions

(1) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

(2) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?

(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.

(7) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.