Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $10164

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 = $10164 – $6600 = $3564

Thus, Simple Interest = $3564

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 × 3564}/_{6600 × 9}

= ³⁵⁶⁴⁰⁰/₅₉₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6600

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

Simple Interest = $3564 (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 $6600

= ⁹/₁₀₀ × 6600

= ^{9 × 6600}/₁₀₀

= ⁵⁹⁴⁰⁰/₁₀₀ = 594

Thus, simple Interest for 1 year = $594

Now,

∵ If the simple Interest is $594, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₄ years

∴ If the simple Interest is $3564, then the time = ¹/₅₉₄ × 3564 years

= ^{1 × 3564}/₅₉₄ years

= ³⁵⁶⁴/₅₉₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?

(3) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?

(4) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

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

(6) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?

(7) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(8) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 6% simple interest?

(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?

(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.