Question

You have $100,000 in an account that earns 2% APR (Compounded monthly)
You want to earn a higher rate of return and therefore are considering two alternative investments. You will put your $100,000 in one of the two new accounts.
Investment 1 will pay you $860 per month for starting next month 120 months.
Investment 2 will pay you $2,600 per month for starting next month 40 months.

Which account should you choose and how much does it increase your net worth?

Group of answer choices

Choose Investment 2 it increases your net worth by $528

Choose Investment 1 it increases your net worth by $544

Choose Investment 2 it increases your net worth by $508

Choose Investment 2 it increases your net worth by $547

Answer 1

APR for account = 2% p.a. compounded monthly

Monthly rate = APR / 12 = (2% /12)

Now we will calculate change in net worth because of investments

Calculating change in Net worth under Investment 1

Investment Amount = 100000

Change in Net worth = Sum of Present value of monthly cash inflows received from investment - Investment Amount

where monthly cash inflow = $860 and no of months = 120

We can find the sum of present value of monthly cash inflows received from investment by using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get Sum of present value of monthly cash inflows = $93464.59

Change in Net worth = 93464.59 - 100000 = - $6535.41 = 6535 (rounded to nearest whole dollar)

Hence If investment 1 is undertaken, then Net worth decreases by $6535

Calculating change in Net worth under Investment 2

Investment Amount = 100000

Change in Net worth = Sum of Present value of monthly cash inflows received from investment - Investment Amount

where monthly cash inflow = $2600 and no of months = 40

We can find the sum of present value of monthly cash inflows received from investment by using PV function in excel

Formula to be used in excel: =PV(rate,nper,-pmt)

Using PV function in excel, we get Sum of present value of monthly cash inflows = $100528.11

Change in Net worth = 100528.11 - 100000 = 528.11 = $528 (rounded to nearest whole dollar)

Hence If investment 2 is undertaken, then Net worth increases by $528

So investment 2 should be chosen as it increases net worth by $528

Answer: Choose Investment 2 it increases your net worth by $528