Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $8432

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 = $8432 – $6200 = $2232

Thus, Simple Interest = $2232

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 × 2232}/_{6200 × 6}

= ²²³²⁰⁰/₃₇₂₀₀

= 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) = $6200

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2232 (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 $6200

= ⁶/₁₀₀ × 6200

= ^{6 × 6200}/₁₀₀

= ³⁷²⁰⁰/₁₀₀ = 372

Thus, simple Interest for 1 year = $372

Now,

∵ If the simple Interest is $372, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₂ years

∴ If the simple Interest is $2232, then the time = ¹/₃₇₂ × 2232 years

= ^{1 × 2232}/₃₇₂ years

= ²²³²/₃₇₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(2) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.

(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 3% simple interest?

(7) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.

(8) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.