Question

You are 20 years old now and you will save $10,000 annually for the next 30 years and the interest rate is 9%. How much money you will have when you are 50 years old?

A.	$1,363,075.39
	B.	$899,937.73
	C.	$1,112,577.83
	D.	$998,181.47

What is the PV of $2,000 to be received in 10 years at an interest rate of 8%?

	A.	$980.25
	B.	$926.39
	C.	$783.12
	D.	$1,000

Answer 1

1. Option (A) is correct

Here, the deposits will be same every year, so it is an annuity. Here we will use the future value of annuity formula as per below:

FVA = P * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, P is the periodical amount = $10000, r is the rate of interest = 9% and n is the time period = 50 - 20 = 30

Now, putting these values in the above formula, we get,

FVA = $10000 * ((1 + 9%)³⁰ - 1 / 9%)

FVA = $10000 * ((1 + 0.09)³⁰ - 1 / 0.09)

FVA = $10000 * ((1.09)³⁰ - 1 / 0.09)

FVA = $10000 * ((13.2676784691 - 1 / 0.09)

FVA = $10000 * (12.2676784691 / 0.09)

FVA = $10000 * 136.307538546

FVA = $1363075.39

So, we will have $1363075.39 in the account.

2. Option (B) is correct

Here we will use the following formula:

PV = FV / (1 + r%)ⁿ

where, FV = Future value = $2000, PV = Present value, r = rate of interest = 8%, n= time period =10

now, putting these values in the above equation, we get,

PV = $2000 / (1 + 8%)¹⁰

PV = $2000 / (1 + 0.08)¹⁰

PV = $2000 / (1.08)¹⁰

PV = $2000 / 2.15892499727

PV = $926.39

So, present value is $926.39