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) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.

(2) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.

(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?

(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 4% simple interest for 7 years.

(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 4% simple interest?

(8) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(9) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $9685 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.