Simple Interest
Math MCQs

Question :    How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

Correct Answer  $7550

Solution & Explanation

Solution

Given,

Amount (A) = $8305

Rate of Simple Interest (R) = 2%

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

$8305 = P (1 + 2% × 5)

⇒ $8305 = P (1 + ²/₁₀₀ × 5)

⇒ $8305 = P (1 + ^{2 × 5}/₁₀₀)

⇒ $8305 = P (1 + ¹⁰/₁₀₀)

⇒ $8305 = P (^{100 + 10}/₁₀₀)

⇒ $8305 = P × ¹¹⁰/₁₀₀

⇒ P × ¹¹⁰/₁₀₀ = $8305

⇒ P = ⁸³⁰⁵/_¹¹⁰/100

⇒ P = 8305 × ¹⁰⁰/₁₁₀

⇒ P = ^{8305 × 100}/₁₁₀

⇒ P = ⁸³⁰⁵⁰⁰/₁₁₀

⇒ P = $7550

Thus, the sum borrowed (P) = $7550 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 = 2% per annum

Thus, Interest = 2% of principal

⇒ Interest = 2% of 100 = 2

Thus, Simple Interest for 1 year = 2

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 × 2 = 10

Thus, simple interest for 5 years = 10

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 10 = 110

Calculation of the Principal

Now,

∵ If the Amount is 110, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₀

∴ If the Amount is 8305, then the Principal = ¹⁰⁰/₁₁₀ × 8305

= ^{100 × 8305}/₁₁₀

= ⁸³⁰⁵⁰⁰/₁₁₀

= 7550

Thus, Principal = $7550

Thus, the sum borrowed = $7550 Answer

Similar Questions

(1) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 6% simple interest?

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 6% simple interest?

(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?

(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(5) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 5% simple interest.

(7) How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?

(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.

(9) 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.

(10) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.