Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $6532

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 = $6532 – $4600 = $1932

Thus, Simple Interest = $1932

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 × 1932}/_{4600 × 6}

= ¹⁹³²⁰⁰/₂₇₆₀₀

= 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) = $4600

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

Simple Interest = $1932 (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 $4600

= ⁶/₁₀₀ × 4600

= ^{6 × 4600}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = 276

Thus, simple Interest for 1 year = $276

Now,

∵ If the simple Interest is $276, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₆ years

∴ If the simple Interest is $1932, then the time = ¹/₂₇₆ × 1932 years

= ^{1 × 1932}/₂₇₆ years

= ¹⁹³²/₂₇₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) How much loan did Nancy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7687.5 to clear it?

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.

(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.

(6) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?

(7) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(9) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.