Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $9955

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 = $9955 – $5500 = $4455

Thus, Simple Interest = $4455

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 × 4455}/_{5500 × 9}

= ⁴⁴⁵⁵⁰⁰/₄₉₅₀₀

= 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) = $5500

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

Simple Interest = $4455 (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 $5500

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = 495

Thus, simple Interest for 1 year = $495

Now,

∵ If the simple Interest is $495, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₅ years

∴ If the simple Interest is $4455, then the time = ¹/₄₉₅ × 4455 years

= ^{1 × 4455}/₄₉₅ years

= ⁴⁴⁵⁵/₄₉₅ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Edward borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9120 to clear it?

(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 9% simple interest?

(3) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?

(5) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(7) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 4 years.

(9) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.