Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $9200

Rate of Simple Interest (R) = 3%

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

$9200 = P (1 + 3% × 5)

⇒ $9200 = P (1 + ³/₁₀₀ × 5)

⇒ $9200 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9200 = P (1 + ¹⁵/₁₀₀)

⇒ $9200 = P (^{100 + 15}/₁₀₀)

⇒ $9200 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9200

⇒ P = ⁹²⁰⁰/_¹¹⁵/100

⇒ P = 9200 × ¹⁰⁰/₁₁₅

⇒ P = ^{9200 × 100}/₁₁₅

⇒ P = ⁹²⁰⁰⁰⁰/₁₁₅

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 9200, then the Principal = ¹⁰⁰/₁₁₅ × 9200

= ^{100 × 9200}/₁₁₅

= ⁹²⁰⁰⁰⁰/₁₁₅

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?

(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?

(4) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.

(6) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.

(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(8) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.

(9) How much loan did Anthony borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7560 to clear it?

(10) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?