Question

suppose you have 13000 to invest. Which of the two rates will yield the largest amount in 1 year 10% compounded daily or 9.86% compounded continuously

Answer 1

Given:

Invest Amount = 13000

Time = 1 year

Compound daily = 10%

Compound continuously = 9.86%

Sol:

The compound interest formula is:

`A=P(1+(r)/(n))^(nt)`

Where,

`\begin{gathered} A=\text{ Amount after ''n'' year.} \\ P=\text{ Principal amount } \\ r=\text{ Rate} \\ n=\text{ Number of time in compounded per year.} \\ t=\text{ Number of years} \end{gathered}`
`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=13000(1+(0.1)/(365))^(365*1) \\ \\ A=13000(1+2.74*10^(-4))^(365) \\ \\ A=13000(1.000274)^(365) \\ \\ A=13000*1.1052 \\ \\ A=14367.025 \\ \end{gathered}`

So the amount is 14367.025

(b)

When compounded continuously.

`\begin{gathered} A=P* e^(rt) \\ \end{gathered}`
`\begin{gathered} A=P* e^(rt) \\ \\ A=13000* e^((0.0986*1)) \\ \\ A=13000*2.68 \\ \\ A=34846.38 \end{gathered}`

So the amount is 34846.38