Simple Interest
Math MCQs

Question :    Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $9983 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6700

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

Amount (A) = $9983

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 = $9983 – $6700 = $3283

Thus, Simple Interest = $3283

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 × 3283}/_{6700 × 7}

= ³²⁸³⁰⁰/₄₆₉₀₀

= 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) = $6700

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

Simple Interest = $3283 (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 $6700

= ⁷/₁₀₀ × 6700

= ^{7 × 6700}/₁₀₀

= ⁴⁶⁹⁰⁰/₁₀₀ = 469

Thus, simple Interest for 1 year = $469

Now,

∵ If the simple Interest is $469, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₉ years

∴ If the simple Interest is $3283, then the time = ¹/₄₆₉ × 3283 years

= ^{1 × 3283}/₄₆₉ years

= ³²⁸³/₄₆₉ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.

(2) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(3) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(5) How much loan did James borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5500 to clear it?

(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 8 years.

(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(8) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.