Simple Interest
Math MCQs

Question :    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.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $6556

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 = $6556 – $4400 = $2156

Thus, Simple Interest = $2156

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 × 2156}/_{4400 × 7}

= ²¹⁵⁶⁰⁰/₃₀₈₀₀

= 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) = $4400

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2156 (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 = 7% of Principal

= 7% of $4400

= ⁷/₁₀₀ × 4400

= ^{7 × 4400}/₁₀₀

= ³⁰⁸⁰⁰/₁₀₀ = 308

Thus, simple Interest for 1 year = $308

Now,

∵ If the simple Interest is $308, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₈ years

∴ If the simple Interest is $2156, then the time = ¹/₃₀₈ × 2156 years

= ^{1 × 2156}/₃₀₈ years

= ²¹⁵⁶/₃₀₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.

(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 9% simple interest?

(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.

(5) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.

(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?

(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?