• You deposit $5,000 into a 3-year certificate of deposit account that pays an annual compound interest of 3.0%. When the CD period is up, you roll the entire balance over into another 3-year CD paying 3.5%. How much will you have at the end of 6 years?
P = Po(1+r)^n.
r = 3% / 100% = 0.03 = Annual % rate expressed as a deciml.
n = 1Comp/yr * 3yrs = 3 Compounding periods.
P = 5000(1.03)^3 = $5463.64 in 3 yrs.
P = Po(1+r)^n.
Po = 5463.64.
r = 0.035.
n = 3.
Plug the given values into the given Eq.
Answer: P = $6057.64 In 6 yrs.
To find out how much you will have at the end of 6 years, we need to calculate the future value of the initial deposit and the future value of the rolled-over deposit separately, and then add them together.
For the initial deposit of $5,000, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
Where:
FV = Future Value
PV = Present Value (initial deposit)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = number of years
For the initial deposit of $5,000 with an interest rate of 3.0% compounded annually for 3 years:
FV1 = $5,000 * (1 + 0.03/1)^(1*3)
= $5,000 * (1 + 0.03)^3
= $5,000 * (1.03)^3
= $5,000 * 1.092727
≈ $5,463.64
Next, we calculate the future value of the rolled-over deposit. The initial deposit of $5,463.64 becomes the present value for the second CD.
For the rolled-over deposit of $5,463.64 with an interest rate of 3.5% compounded annually for another 3 years:
FV2 = $5,463.64 * (1 + 0.035/1)^(1*3)
= $5,463.64 * (1 + 0.035)^3
≈ $5,463.64 * 1.11266884
≈ $6,082.50
Finally, we add the future values of both deposits:
Total Future Value = FV1 + FV2
= $5,463.64 + $6,082.50
≈ $11,546.14
Therefore, at the end of 6 years, you will have approximately $11,546.14 in your CD account.