Simple Interest
Math MCQs

Question :    How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

Correct Answer  $7900

Solution & Explanation

Solution

Given,

Amount (A) = $9480

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

$9480 = P (1 + 4% × 5)

⇒ $9480 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9480 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9480 = P (1 + ²⁰/₁₀₀)

⇒ $9480 = P (^{100 + 20}/₁₀₀)

⇒ $9480 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9480

⇒ P = ⁹⁴⁸⁰/_¹²⁰/100

⇒ P = 9480 × ¹⁰⁰/₁₂₀

⇒ P = ^{9480 × 100}/₁₂₀

⇒ P = ⁹⁴⁸⁰⁰⁰/₁₂₀

⇒ P = $7900

Thus, the sum borrowed (P) = $7900 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 9480, then the Principal = ¹⁰⁰/₁₂₀ × 9480

= ^{100 × 9480}/₁₂₀

= ⁹⁴⁸⁰⁰⁰/₁₂₀

= 7900

Thus, Principal = $7900

Thus, the sum borrowed = $7900 Answer

Similar Questions

(1) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 10% simple interest for 3 years.

(3) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9062.5 to clear it?

(4) James had to pay $3450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 8% simple interest?

(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.

(7) 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.

(8) Donald had to pay $5175 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.

(10) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?