Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $8036

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 = $8036 – $4900 = $3136

Thus, Simple Interest = $3136

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 × 3136}/_{4900 × 8}

= ³¹³⁶⁰⁰/₃₉₂₀₀

= 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) = $4900

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3136 (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 = 8% of Principal

= 8% of $4900

= ⁸/₁₀₀ × 4900

= ^{8 × 4900}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3136, then the time = ¹/₃₉₂ × 3136 years

= ^{1 × 3136}/₃₉₂ years

= ³¹³⁶/₃₉₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(2) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.

(4) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(5) 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.

(6) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(7) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?

(10) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.