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) 1.012^2 times B
b) 1.012^3 times B
c) B+7 times 1.012
d) B + 2 times 1.012
e) B+ 3 times 1.012
f) 1.012^7 times B
f) 1.012^7 times B
When a CD earns interest that compounds annually, the formula to calculate the future value is:
Future Value = Present Value x (1 + i)^n
Where i is the interest rate and n is the number of years.
In this case, the interest rate is 1.2% or 0.012, so the formula becomes:
Future Value = B x (1 + 0.012)^5
Future Value = B x (1.012)^5
To calculate the CD's value when it matures in 5 years, we use the formula above:
Future Value = B x (1.012)^5
Future Value = 1.012^5 times B
Future Value = 1.06136 times B
So, the CD's value when it matures in 5 years will be 1.012^5 times B, which is option f).