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?
To find the CD's value after 5 years, we need to calculate the compound interest. 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)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested for
In this case, the principal investment amount (P) is B, the annual interest rate (r) is 1.2% or 0.012, the number of times interest is compounded per year (n) is 1 (compounded annually), and the number of years (t) is 5.
Therefore, the formula becomes:
A = B(1 + 0.012/1)^(1*5)
Simplifying,
A = B(1 + 0.012)^5
A = B(1.012)^5
Now we can calculate the CD's value when it matures in 5 years.