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 $6683 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $6683

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 = $6683 – $4100 = $2583

Thus, Simple Interest = $2583

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 × 2583}/_{4100 × 9}

= ²⁵⁸³⁰⁰/₃₆₉₀₀

= 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) = $4100

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

Simple Interest = $2583 (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 $2583, then the time = ¹/₃₆₉ × 2583 years

= ^{1 × 2583}/₃₆₉ years

= ²⁵⁸³/₃₆₉ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?

(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(3) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.

(5) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(10) Emily had to pay $5462.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.