Simple Interest
Math MCQs

Question :    John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4400

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $6512

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 = $6512 – $4400 = $2112

Thus, Simple Interest = $2112

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 × 2112}/_{4400 × 8}

= ²¹¹²⁰⁰/₃₅₂₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = 8% per annum

Simple Interest = $2112 (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 = 8% of Principal

= 8% of $4400

= ⁸/₁₀₀ × 4400

= ^{8 × 4400}/₁₀₀

= ³⁵²⁰⁰/₁₀₀ = 352

Thus, simple Interest for 1 year = $352

Now,

∵ If the simple Interest is $352, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₂ years

∴ If the simple Interest is $2112, then the time = ¹/₃₅₂ × 2112 years

= ^{1 × 2112}/₃₅₂ years

= ²¹¹²/₃₅₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.

(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(3) How much loan did Joseph borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7125 to clear it?

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

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

(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.

(7) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(9) In how much time a principal of $3150 will amount to $3528 at a simple interest of 4% per annum?

(10) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.