Question

If 39100 dollars is invested at an interest rate of 5 percent per year, find the value of the investment at the end of 5 years for the following compounding methods.Round all answers to the nearest penny.(a) Annual:Your answer is $ (b) Semiannual:Your answer is $ (c) Monthly:Your answer is $ (d) Daily:Your answer is $

Answer 1

Answer:
`\begin{gathered} a)\text{ \$49902.61} \\ b)\text{ \$50051.31} \\ c)\text{ \$50179.32} \\ d)\text{ \$50204.53} \end{gathered}`

Step-by-step explanation:

Amount invested = $39,100

rate = 5% = 0.05

t = Time = 5 years

To determine the compounding methods, we will apply the compound interest formula:

`$$FV\text{ = P(1 +}(r)/(n))^(nt)$$`
`\begin{gathered} a)\text{ Annual compounding:} \\ n\text{ = number of times compounded = annual} \\ n\text{ = 1} \\ FV\text{ = 39100\lparen1 + }(0.05)/(1))^(1*5) \\ FV=\text{ 39000\lparen1.05\rparen}^5 \\ FV=\text{ 49902.61} \\ To\text{ the nearest penny, the future value is \$49902.61} \end{gathered}`

`\begin{gathered} b)\text{ Semi-annual compounding:} \\ n\text{ = 2} \\ FV\text{ = 39100\lparen1 + }(0.05)/(2))^(2*5) \\ FV=\text{ 39000\lparen1.025\rparen}^(10) \\ FV=\text{ 50051.31} \\ To\text{ the nearest penny, the future value is \$50051.31} \end{gathered}`

`\begin{gathered} c)\text{ Monthly compounding:} \\ n\text{ = 12} \\ FV\text{ = 39100\lparen1 + }(0.05)/(12))^(12*5) \\ FV=\text{ 39100\lparen1.00417\rparen}^(60) \\ FV=\text{ 50179.32} \\ To\text{ the nearest penny, the future value is \$50179.32} \end{gathered}`
`\begin{gathered} d)\text{ }Daily\text{ compounding:} \\ n\text{ = 365} \\ FV\text{ = 39100\lparen1 + }(0.05)/(365))^(365*5) \\ FV=50204.53 \\ To\text{ the nearest penny, the future value is \$50204.53} \end{gathered}`