Question

3) Frank is considering the following two investment options that his broker has offered. Which one should he choose and why?
(show work)

Option 1) Deposit $50,000 today, and for the next 10 years make a payment of $1,000 at the end of each month. After 10 years, you will be able to withdraw a total of $300,000 from your account.

Option 2) Deposit $80,000 today, and for the next 10 years make a payment of $10,000 at the end of each year. After 10 years, you will be able to withdraw a total of $300,000 from your account.

Answer 1

In the given question, future value of both the options need to be calculated. In order to calculate future value, interest rate is required which is not given. However, Future Value for both the options are given, so we need to calculate the interest rate for both the options and the option with higher interest rate should be chosen.

There are two formulas to calculate future value depending upon stream of cash-flows. Both the formulas are mentioned below and will be used.

Formula to calculate future value of one single deposit: FV = PV x (1+r)ⁿ

Formula to calculate future value of equal periodic cash-flow: FV = Pmt x ((1+r)ⁿ -1))/r)

So, Formula to calculate future value in given options:
FV = [PV x (1+r)ⁿ] + [Pmt x ((1+r)ⁿ -1))/r)]

Where, “PV” is Present Value, “Pmt” is periodic cash deposit, “r” is interest rate and “n” is number of periods.

Option 1:

Future Value of $50,000 deposited today:

PV = $50,000
r = ?
n = 11

Future Value of $1,000 deposited at the end of each month:

Pmt = $1,000
r = ? (Monthly interest rate)
n = 10 Years x 12 = 120 months

Net Future Value = $300,000

300,000 = [$50,000 x (1+r)¹¹] + [$1,000 x ((1+r/12)¹²⁰ -1))/ r/12)

r = 8.021%

Option 2:

Future Value of $80,000 deposited today:

PV = $80,000
r = ?
n = 11

Future Value of $1,000 deposited at the end of each month:

Pmt = $1,000
r = ? (Annual interest rate)
n = 10

Net Future Value = $300,000

300,000 = [$80,000 x (1+r)¹¹] + [$1,000 x ((1+r)¹⁰ -1))/ r)

r = 6.722%

Since the effective interest rate earned is higher in Option 1, Frank should go with that.