Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $8869

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 = $8869 – $4900 = $3969

Thus, Simple Interest = $3969

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 × 3969}/_{4900 × 9}

= ³⁹⁶⁹⁰⁰/₄₄₁₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 9% per annum

Simple Interest = $3969 (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 $4900

= ⁹/₁₀₀ × 4900

= ^{9 × 4900}/₁₀₀

= ⁴⁴¹⁰⁰/₁₀₀ = 441

Thus, simple Interest for 1 year = $441

Now,

∵ If the simple Interest is $441, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₁ years

∴ If the simple Interest is $3969, then the time = ¹/₄₄₁ × 3969 years

= ^{1 × 3969}/₄₄₁ years

= ³⁹⁶⁹/₄₄₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.

(3) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 3 years.

(6) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?

(8) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(9) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 9% simple interest?

(10) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.