Jon went to his local bank and deposited money in a certificate of deposit, or CD for short. A CD is a type of savings account that does not allow withdrawals until a set amount of time has passed.
The CD that Jon opened earns interest that compounds annually at a rate of 1.2%. If you know the CD's value is equal to B after 2 years, what will the CD's value be when it matures in 5 years?
a. 1.012^7 * B
b. 1.012^3 * B
c. 1.012^2 * B
d. B + 7 * 1.012
e. B + 2 * 1.012
f. B + 3 * 1.012
To find the CD's value when it matures in 5 years, we need to calculate the value after 5 years using the compound interest formula.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested or borrowed for
In this case, the principal investment amount is B, the annual interest rate (r) is 1.2% or 0.012 as a decimal, n is 1 (since interest compounds annually), and t is 5 years.
So, plugging in the values into the formula:
A = B(1 + 0.012/1)^(1 * 5)
= B(1 + 0.012)^5
= B(1.012)^5
Therefore, the CD's value when it matures in 5 years is:
1.012^5 * B
The correct answer is:
a. 1.012^7 * B