Question

Complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per year. (Round your answers to the nearest cent.)

Answer 1

Note: Compound Interest Formula

From the question

Principal = $1500

Rate = 4.5% = 0.045

Time = 25 years

When n = 1

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=1500(1+(0.045)/(1))^(25) \\ \\ A=4508.15\text{ dollars \lparen to the nearest cent\rparen} \end{gathered}`

When n = 4

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=1500(1+(0.045)/(4))^(100) \\ \\ A=4591.40\text{ dollars \lparen to the nearest cent\rparen} \end{gathered}`

When n = 12

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=1500(1+(0.045)/(12))^(25*12) \\ \\ A=4610.61\text{ dollars \lparen to the nearest cent\rparen} \end{gathered}`

When n = 365

`\begin{gathered} A=P(1+(r)/(n))^(nt) \\ \\ A=1500(1+(0.045)/(365))^(25*365) \\ \\ A=4620.00\text{ dollars \lparen to the nearest cent\rparen} \end{gathered}`

For compounded continuously

`\begin{gathered} A=Pe^(rt) \\ A=1500e^((0.045*25)) \\ \\ A=4620.33\text{ dollars \lparen to the nearest cent\rparen} \end{gathered}`