Answer:
a. The CD will worth<u> $35,311 </u>in five years.
b. It will take <u>12.44 years </u>for the account to be worth $45,000.
Explanation:
a) If $30,000 is invested in this CD, how much will it be worth in 5 years?(Round to the nearest cent.)
This can be determined using the formula for calculating the future value (FV) compounding formula as follows:
FV = PV * e^(rn) ................................... (1)
FV = Future value in five years = ?
PV = Present value of amount invested = $30,000
e = Mathematical constant approximated as 2.7183
r = Interest rate = 3.26%, or 0.0326
n = number of years = 5
Substituting the values into equation (1), we have:
FV = $30,000 * 2.7183^(0.0326 * 5)
FV= $35,311
Therefore, the CD will worth<u> $35,311 </u>in five years.
(b) How long will it take for the account to be worth $45,000?(Round to two decimal places as needed)
Also, using equation (1) part a, we have:
FV = Future value in n years = $45,000
PV = Present value of amount invested = $30,000
e = Mathematical constant approximated as 2.7183
r = Interest rate = 3.26%, or 0.0326
n = number of years it will take to have $45,000 = ?
Substituting the values into equation (1), we have:
$45,000 = $30,000 * 2.7183^(0.0326 * n)
$45,000 / $30,000 = 2.7183^(0.0326 * n)
1.50 = 2.7183^(0.0326 * n)
Loglinearise both sides and solve for n, we have:
Log(1.50) = (0.0326 * n)Log(2.7183)
0.176091259055681 = 0.0326 * n * 0.434297385124509
0.176091259055681 = n * 0.014158094755059
n = 0.176091259055681 / 0.014158094755059
n = 12.44 years
Therefore, it will take <u>12.44 years </u>for the account to be worth $45,000.
