Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $7320

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

$7320 = P (1 + 4% × 5)

⇒ $7320 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7320 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7320 = P (1 + ²⁰/₁₀₀)

⇒ $7320 = P (^{100 + 20}/₁₀₀)

⇒ $7320 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7320

⇒ P = ⁷³²⁰/_¹²⁰/100

⇒ P = 7320 × ¹⁰⁰/₁₂₀

⇒ P = ^{7320 × 100}/₁₂₀

⇒ P = ⁷³²⁰⁰⁰/₁₂₀

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 7320, then the Principal = ¹⁰⁰/₁₂₀ × 7320

= ^{100 × 7320}/₁₂₀

= ⁷³²⁰⁰⁰/₁₂₀

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 7 years.

(3) If James borrowed $3000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(5) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?

(6) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.

(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 7% simple interest?

(8) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.

(10) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 5% simple interest?