Question

Find the missing values assuming continuously compounded interest. (Round your answers to two decimal places.)
Initial Annual
Investment |% Rate
Time to
Double
Amount After
10 Years
$2000
5.6%
yr $

Answer 1

Answer:

$3448.81

Step-by-step explanation:

Using the compound interest formula to calculate the amount compounded after 10years.

$A = P(1+r)^{nt}$

P = principal  = $2000

r = rate (in %) = 5.6%

t = time (in years) = 10years

n = 1year = time used in compounding

$A = 2000(1+0.056)^{10} \\A = 2000(1.056)^{10}\\A = 2000*1.7244046\\A = 3448.81 (to\ 2dp)$

Amount compounded after 10 years is $3448.81

Answer 2

The number of years it would take the investment to double is 12.38 years.

The amount after 10 years is  $21,151.95.

The formula used to determine the future value of an investment when interest is compounded continuously is:

FV =  A x $e^{r}$ x N

• A= amount invested = $2000
• e = 2.7182818
• N = number of years
• r = interest rate = 5.6%
• FV = future value

Time to double :

FV = $4000

FV / PV = 2

n = log(2) ÷ log(e) ÷ 0.056 = 12.38 years

Amount after 10 years

$2000 x $e^{r}$ x 10 = $21,151.95

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