Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $10212

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 = $10212 – $6900 = $3312

Thus, Simple Interest = $3312

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 × 3312}/_{6900 × 6}

= ³³¹²⁰⁰/₄₁₄₀₀

= 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) = $6900

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

Simple Interest = $3312 (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 $6900

= ⁶/₁₀₀ × 6900

= ^{6 × 6900}/₁₀₀

= ⁴¹⁴⁰⁰/₁₀₀ = 414

Thus, simple Interest for 1 year = $414

Now,

∵ If the simple Interest is $414, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₄ years

∴ If the simple Interest is $3312, then the time = ¹/₄₁₄ × 3312 years

= ^{1 × 3312}/₄₁₄ years

= ³³¹²/₄₁₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 8 years.

(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?

(4) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?

(7) How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?

(8) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.