Question

The value of an old bike decreases every year at the rate of 4% over that of the poisons year. If its value at the end of three years is 13824, then find it’s passed value.
A) 15625
B) 14525
C) 16625
D) 15425

Answer 1

Hint: Use the formula $A=P{{\left( 1-{}^{R}/{}_{100} \right)}^{n}}$. Simple interest is calculated by multiplying the daily interest rate by the principal, by the number of days that elapse between payments. The simple interest formula is I = P x R x T. Compute compound interest using the following formula: $\text{A=P}\left(1+\dfrac{r}{n}\right)^{\text{nt}}$. Assume the amount borrowed, P, is $10,000. The annual interest rate, r, is 0.05, and the number of times interest is compounded in a year, n, is 4.

Complete step by step solution: Simple Interest, SI = P x R x T / 100, where P is the principal, R is the rate of interest per unit time period and T is the time period. As the name suggests, a daily simple interest loan means that interest is accruing every day. However, since that interest is only calculated on the current unpaid principal, your lender splits your payment amount between the interest owed and a portion of the principal balance.
Rate of decrease of value $=4%$ when value depreciates, value $\text{A}\ \text{=}\ \text{P}\ {{\left( \text{1-}\dfrac{\text{R}}{\text{100}} \right)}^{n}}$
Given.
Value $\begin{align}
  & =\ \text{Rs}\ \text{13824}\text{.} \\
 & \\
\end{align}$
So,$\text{P}\times {{\left( 1-\dfrac{4}{100} \right)}^{3}}=\text{Rs}\ \text{13824}$
$\Rightarrow \text{P}\times \text{0}\text{.96}\times \text{0}\text{.96}\times \text{0}\text{.96}\ \text{=}\ \text{Rs13824}$
$\Rightarrow \ \text{P}\ \text{=}\ \text{Rs15625}\text{.}$

Hence, the answer to this question is 15625, A.option

Note: In this type of question, we need to know about the percentage of decrease and increase over time. Simple interest is significantly beneficial to borrowers who make prompt payments. Late payments are disadvantageous as more money will be directed toward the interest and less toward the principal. Simple interest applies mostly to short-term loans, such as personal loans.