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) Nancy had to pay $4648 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.

(3) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 10% simple interest?

(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?

(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(7) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.

(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.

(10) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.