Question

Regina Henry deposited $20,000 in a money market certificates that provides interest of 10% compound and quarterly if the amount is maintained for 3 years. How much will Regina have at the end of 3 years? Will Smith will receive $80,000 5 years from now, from a trust fund established by his father. Assuming the appropriate interest rate for discounting is 12% (compound that semiannually), what is the present value of this amount today?

Answer 1

Regina: Final amount=$62,769

Will Smith: Present value: $213,216

Step-by-step explanation:

Regina:

Compound quarterly means that each quarter of the year ( every three months) she will receive a 10% interest rate of her deposit. To convert this periodic rate to an annual rate( because the problem ask you about years) you use this formula :

Annual rate= ((1+Periodic rate)^(# periods))-1

In this case the number of periods means the number of quarters a year have, which is 4

Annual rate= ((1+10%)^(4))-1= 46.41%

To find the final amount Regina has after 3 year we use this formula:

Final Capital (FC)= Initial Capital (IC)*[(1+interest(i))]^(number of periods(n))

FC= $20,000*[(1+46.41%)^3]

FC=$62,769 I attached an excel figure which shows a more detailed data.

Will Smith

Semiannually means that every 6 months Will Smith will receive a 12% interest rate of the initial investment. To convert this periodic rate to an annual rate you use the same above formula:

Annual rate= ((1+Periodic rate)^(# periods))-1

In each year Will will receive twice the interest rate over the initial investment

Annual rate = ((1+12%)^(2))-1

Annual rate= 25.44%

The present value of $80,000 from now to 5 years is calculated using the formula attached, but I used Excel. First you have to copy all the cash flows of the 5 years. Then, you set the interest rate that in this case is the one that you found above( 25.44%). Finally you use the financial formula "NPV" in this way:

"=NPV(25.44%;C4:C8)" I used C4:C8 because in those excel cells i copied the cash flows.

I got that the present value of this amount is $213,216