Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 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) = 6% per annum

Amount (A) = $8976

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 = $8976 – $6600 = $2376

Thus, Simple Interest = $2376

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 × 2376}/_{6600 × 6}

= ²³⁷⁶⁰⁰/₃₉₆₀₀

= 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) = 6% per annum

Simple Interest = $2376 (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 $6600

= ⁶/₁₀₀ × 6600

= ^{6 × 6600}/₁₀₀

= ³⁹⁶⁰⁰/₁₀₀ = 396

Thus, simple Interest for 1 year = $396

Now,

∵ If the simple Interest is $396, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₆ years

∴ If the simple Interest is $2376, then the time = ¹/₃₉₆ × 2376 years

= ^{1 × 2376}/₃₉₆ years

= ²³⁷⁶/₃₉₆ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.

(3) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?

(5) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(6) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(8) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(9) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.