Question

A.

Two years ago, you opened an investment account and deposited $6,000. One year ago, you added another $2,100 to the account. Today, you are making a final deposit of $8,000. How much will you have in this account 3 years from today if you earn a 14.10 percent rate of return? B. How much more current value does a perpetuity of $250 a year have as compared to an annuity of $250 a year for 50 years given an interest rate of 8.5 percent? C. What is the present value of an annuity due if the payments are $71 a month for 72 months at a monthly interest rate of 1.5 percent?

Answer 1

Deposit	years	Interest rate	FV factor	FV of deposit
6000	5	14.1%	1.933874212	11603.25
2100	4	14.1%	1.694894138	3559.28
8000	3	14.1%	1.485446221	11883.57
			Total	27046.09

After 3 years balance in the account will be $27046.09

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We need to find PV of both investments

Perpetuity is equal amount of cash flow that is received in future for infinite period.

If periodic payment is P, and interest rate is r then present value of perpetuity is

PV of perpetuity= P/ r

Let's put all the values in the formula

PV of perpetuity= 250/ 0.085

= $2941.18

Present value of annuity is the present worth of cash flows that is to be received in the future, if future value is known, rate of interest in r and time is n then PV of annuity is

PV of annuity = P[1- (1+ r)^-n]/ r

= 250[1- (1+ 0.085)^-50]/ 0.085

= 250[1- (1.085)^-50]/ 0.085

= 250[1- 0.016924392582173]/ 0.085

= 250[0.983075607417827/ 0.085]

= 250[11.5655953813862]

= $2891.4

Perpetuity has higher balance than annuity

Difference = $2941.18 - $2891.4 = $49.78

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Present Value of an annuity due is used to determine the present value of a stream of equal payments where the payment occurs at the beginning of each period.

If,

Periodic payment (P) = 71

Interest rate (i) = 0.015

Time period (n) = 72

Then PV of annuity due = P * (1 + i) [1 - {(1+ i)^-n}/i]

Lets put all the values in the formula to find PV of annuity due,

PV of annuity due = 71* (1 + 0.015) [{1- (1 + 0.015)^- 72}/ 0.015]

                                      = 71* (1.015) [{1- (1.015)^- 72}/ 0.015]

                                      = 72.065[{1- 0.3423299984}/ 0.015]

                                      = 72.065[0.6576700016/ 0.015]

                                      = 72.065* 43.84467

                                      = 3159.66614

So PV of annuity due is $3159.67

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Hope this answer your query.

Feel free to comment if you need further assistance. J