Simple Interest
Math MCQs

Question :    How much loan did Betty borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7500 to clear it?

Correct Answer  $6250

Solution & Explanation

Solution

Given,

Amount (A) = $7500

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

$7500 = P (1 + 4% × 5)

⇒ $7500 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7500 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7500 = P (1 + ²⁰/₁₀₀)

⇒ $7500 = P (^{100 + 20}/₁₀₀)

⇒ $7500 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7500

⇒ P = ⁷⁵⁰⁰/_¹²⁰/100

⇒ P = 7500 × ¹⁰⁰/₁₂₀

⇒ P = ^{7500 × 100}/₁₂₀

⇒ P = ⁷⁵⁰⁰⁰⁰/₁₂₀

⇒ P = $6250

Thus, the sum borrowed (P) = $6250 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 7500, then the Principal = ¹⁰⁰/₁₂₀ × 7500

= ^{100 × 7500}/₁₂₀

= ⁷⁵⁰⁰⁰⁰/₁₂₀

= 6250

Thus, Principal = $6250

Thus, the sum borrowed = $6250 Answer

Similar Questions

(1) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 3% simple interest for 4 years.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 2% simple interest?

(5) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.

(6) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.

(7) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.