Please show all Calculations You open a money market account with S2,000 that pa

Question

Please show all Calculations

You open a money market account with S2,000 that pays an interest rate of 6% compounded continuously. The year after (next year) you deposit $1000 and the [interest rate now pays 8% compounded continuously. At the end of the third year you decide to withdraw half of the money that has accumulated into the account? I low much will be the amount that you will withdrawal? Immediately after you withdraw half of you balance the interest rate drops to 4% discrete compounded, and remains the same for the rest of the planning horizon. You make an extra deposit of $500 a year later, and then retire the balance at the end of year 6. How much will be in the account at the end of year 6?

Explanation / Answer

a. Formula for continuous compunding: amount = principal * e^(r*t)

amount = $2000. r = 6%.

Now, you have deposited $2000 now. amount after 1 year will be: 2000*e^(6%*1)

= 2,000*2.718^(0.06) = 2,000*1.06182 = $2123.66

Now next year i.e start of year 1, you add $1,000. Total principal at the start of year 1 = 2123.66+1000 = $3,123.66

Now the withdrawal is made at the end of the 3rd year. Thus t = 3 years (year 1, 2 and 3). and n = 8%

amount = 3123.66*2.718^(8%*3) = $3970.85

half of this amount = 3970.85/2 = $1985.425

b. now the money left at the end of 3 years = 1985.425.

And compounding is discrete (i am assuming that compounding is annual).

r = 4%. amount after 1 year i.e end of 4th year = 1985.425*(1+4%)^1 = $2064.84

Now extra $500 is deposited now. Total money at the end of 4th year = 2064.84+500 = 2564.84

Now, n = 2 (year 5 and year 6). r= 4%

amount at the end of year 6 = 2564.84*(1+4%)^2 = 2564.84*1.0816 = $2,774.13

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