Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7380 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7380

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

$7380 = P (1 + 4% × 5)

⇒ $7380 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7380 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7380 = P (1 + ²⁰/₁₀₀)

⇒ $7380 = P (^{100 + 20}/₁₀₀)

⇒ $7380 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7380

⇒ P = ⁷³⁸⁰/_¹²⁰/100

⇒ P = 7380 × ¹⁰⁰/₁₂₀

⇒ P = ^{7380 × 100}/₁₂₀

⇒ P = ⁷³⁸⁰⁰⁰/₁₂₀

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 7380, then the Principal = ¹⁰⁰/₁₂₀ × 7380

= ^{100 × 7380}/₁₂₀

= ⁷³⁸⁰⁰⁰/₁₂₀

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 4 years.

(2) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(3) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.

(4) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(6) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?

(7) What amount will be due after 2 years if William borrowed a sum of $3250 at a 8% simple interest?

(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?

(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.