Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $8772

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 = $8772 – $5100 = $3672

Thus, Simple Interest = $3672

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 × 3672}/_{5100 × 9}

= ³⁶⁷²⁰⁰/₄₅₉₀₀

= 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) = $5100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3672 (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 = 9% of Principal

= 9% of $5100

= ⁹/₁₀₀ × 5100

= ^{9 × 5100}/₁₀₀

= ⁴⁵⁹⁰⁰/₁₀₀ = 459

Thus, simple Interest for 1 year = $459

Now,

∵ If the simple Interest is $459, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₉ years

∴ If the simple Interest is $3672, then the time = ¹/₄₅₉ × 3672 years

= ^{1 × 3672}/₄₅₉ years

= ³⁶⁷²/₄₅₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(2) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?

(3) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?

(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(6) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.

(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 4 years.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8880 to clear the loan, then find the time period of the loan.

(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.