Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $7052

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 = $7052 – $4100 = $2952

Thus, Simple Interest = $2952

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 × 2952}/_{4100 × 9}

= ²⁹⁵²⁰⁰/₃₆₉₀₀

= 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) = $4100

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

Simple Interest = $2952 (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 $4100

= ⁹/₁₀₀ × 4100

= ^{9 × 4100}/₁₀₀

= ³⁶⁹⁰⁰/₁₀₀ = 369

Thus, simple Interest for 1 year = $369

Now,

∵ If the simple Interest is $369, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₉ years

∴ If the simple Interest is $2952, then the time = ¹/₃₆₉ × 2952 years

= ^{1 × 2952}/₃₆₉ years

= ²⁹⁵²/₃₆₉ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.

(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?

(3) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?

(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.

(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?

(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.