Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8584

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 = $8584 – $5800 = $2784

Thus, Simple Interest = $2784

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 × 2784}/_{5800 × 6}

= ²⁷⁸⁴⁰⁰/₃₄₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $5800

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2784 (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 = 6% of Principal

= 6% of $5800

= ⁶/₁₀₀ × 5800

= ^{6 × 5800}/₁₀₀

= ³⁴⁸⁰⁰/₁₀₀ = 348

Thus, simple Interest for 1 year = $348

Now,

∵ If the simple Interest is $348, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₈ years

∴ If the simple Interest is $2784, then the time = ¹/₃₄₈ × 2784 years

= ^{1 × 2784}/₃₄₈ years

= ²⁷⁸⁴/₃₄₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

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

(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.

(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(4) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(5) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.

(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(9) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?

(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.