Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4400

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

Amount (A) = $7964

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 = $7964 – $4400 = $3564

Thus, Simple Interest = $3564

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 × 3564}/_{4400 × 9}

= ³⁵⁶⁴⁰⁰/₃₉₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4400

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

Simple Interest = $3564 (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 $4400

= ⁹/₁₀₀ × 4400

= ^{9 × 4400}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $3564, then the time = ¹/₃₉₆ × 3564 years

= ^{1 × 3564}/₃₉₆ years

= ³⁵⁶⁴/₃₉₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?

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

(3) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?

(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.

(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?

(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.

(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.

(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 2% simple interest?

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.