Question

3. Two years ago, you invested $5,000 in a four-year certificate of deposit (CD). The annual (stated) rate is 4% on the CD and it is compounded quarterly. Rates have increased and you are considering reinvesting in another certificate of deposit. However, if you withdraw the money from the original CD, you suffer a 10% penalty on the entire balance (interest and principal): a. If you make the withdrawal today, how much would you have remaining? (8 Points)

Answer 1

a. First we can use following formula to calculate the future value (FV) of the deposits after 2 years of investments

FV = PV * (1+i) ^n

Where,

Present Value PV = $5,000 (initial amount of investment in CD)

Future value of deposit FV=?

Annual interest rate i =4%; but compounded quarterly therefore quarterly interest rate = 4%/4 = 1% or 0.01

Time period n = 4* 2 years = 8 quarters

Therefore,

FV = $5,000 * (1+ 1%) ^8

= $5,414.28

This future value of investments is consist of interest and principal amount after 2 years of investment

If you will withdraw today then you suffer a penalty of 10% on entire amount

Therefore penalty = $5,414.28 *10% = $541.43

Therefore remaining amount of investment = Total amount at the end of year 2 – penalty for withdrawal

= $5,414.28 -$541.43

= $4,872.86