Question

it you invest $10,427.00 into an account earning an annual nominal interest rate of 4.502%, how much will you have in your account after 11 years if the interest is compounded quarterly? If the interest is compoundedIf interest is compounded quarterly: FV=If interest is compounded continuously: FV = (Note: All answers for FV = should include a dollar sign and be accurate to two decimal places)

Answer 1

a) Future value is $17061.98

b)

Step-by-step explanation:

a) Principal = $10427

rate = 4.502% = 0.04502

time = 11 years

n = number of times compounded = quarterly

n = 4

FV = future value = ?

To get the future value, we will apply compound interest formula:

`FV\text{ = P(1 +}(r)/(n))^(nt)`
`\begin{gathered} FV\text{ = }10427(1\text{ + }(0.04502)/(4))^(4*11) \\ FV\text{ = }10427(1\text{ + }0.011255)^(44) \\ FV\text{ = }10427(1\text{ }.011255)^(44) \end{gathered}`
`\begin{gathered} FV\text{ = }10427(1\text{ }.011255)^(44) \\ FV\text{ = 17061.97}81 \\ \\ FV\text{ = \$17061.98} \end{gathered}`

Future value is $17061.98

b) For continuous compounding, the formula is given by:

`P_t=P_0e^(rt)`
`\begin{gathered} P_t\text{ = future value = ?} \\ r\text{ = rate = 0.04502} \\ t\text{ = 11 years} \\ P_0\text{ = prinicipal = 10427} \end{gathered}`