Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9028

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 = $9028 – $6100 = $2928

Thus, Simple Interest = $2928

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 × 2928}/_{6100 × 8}

= ²⁹²⁸⁰⁰/₄₈₈₀₀

= 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) = $6100

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

Simple Interest = $2928 (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 $6100

= ⁸/₁₀₀ × 6100

= ^{8 × 6100}/₁₀₀

= ⁴⁸⁸⁰⁰/₁₀₀ = 488

Thus, simple Interest for 1 year = $488

Now,

∵ If the simple Interest is $488, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₈ years

∴ If the simple Interest is $2928, then the time = ¹/₄₈₈ × 2928 years

= ^{1 × 2928}/₄₈₈ years

= ²⁹²⁸/₄₈₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?

(2) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?

(3) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?

(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.

(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.

(7) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 9% simple interest?

(9) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.

(10) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.