Simple Interest
Math MCQs

Question :    How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

Correct Answer  $7250

Solution & Explanation

Solution

Given,

Amount (A) = $8700

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

$8700 = P (1 + 4% × 5)

⇒ $8700 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8700 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8700 = P (1 + ²⁰/₁₀₀)

⇒ $8700 = P (^{100 + 20}/₁₀₀)

⇒ $8700 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8700

⇒ P = ⁸⁷⁰⁰/_¹²⁰/100

⇒ P = 8700 × ¹⁰⁰/₁₂₀

⇒ P = ^{8700 × 100}/₁₂₀

⇒ P = ⁸⁷⁰⁰⁰⁰/₁₂₀

⇒ P = $7250

Thus, the sum borrowed (P) = $7250 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 8700, then the Principal = ¹⁰⁰/₁₂₀ × 8700

= ^{100 × 8700}/₁₂₀

= ⁸⁷⁰⁰⁰⁰/₁₂₀

= 7250

Thus, Principal = $7250

Thus, the sum borrowed = $7250 Answer

Similar Questions

(1) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?

(2) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?

(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.

(6) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.

(8) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.

(9) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.