Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6600

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $10758

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10758 – $6600 = $4158

Thus, Simple Interest = $4158

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4158}/_{6600 × 9}

= ⁴¹⁵⁸⁰⁰/₅₉₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6600

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4158 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 9% of Principal

= 9% of $6600

= ⁹/₁₀₀ × 6600

= ^{9 × 6600}/₁₀₀

= ⁵⁹⁴⁰⁰/₁₀₀ = 594

Thus, simple Interest for 1 year = $594

Now,

∵ If the simple Interest is $594, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₄ years

∴ If the simple Interest is $4158, then the time = ¹/₅₉₄ × 4158 years

= ^{1 × 4158}/₅₉₄ years

= ⁴¹⁵⁸/₅₉₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?

(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?

(3) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6267.5 to clear it?

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 10% simple interest?

(7) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?

(9) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.

(10) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.