Simple Interest
Math MCQs

Question :  ( 2 of 10 )  Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $7599

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 = $7599 – $5100 = $2499

Thus, Simple Interest = $2499

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 × 2499}/_{5100 × 7}

= ²⁴⁹⁹⁰⁰/₃₅₇₀₀

= 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) = $5100

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

Simple Interest = $2499 (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 $5100

= ⁷/₁₀₀ × 5100

= ^{7 × 5100}/₁₀₀

= ³⁵⁷⁰⁰/₁₀₀ = 357

Thus, simple Interest for 1 year = $357

Now,

∵ If the simple Interest is $357, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₇ years

∴ If the simple Interest is $2499, then the time = ¹/₃₅₇ × 2499 years

= ^{1 × 2499}/₃₅₇ years

= ²⁴⁹⁹/₃₅₇ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?

(4) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 4 years.

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.

(6) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.

(8) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(9) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.