niquelove
contestada

Morgan wants to purchase a home in six years. He will contribute $3500 each year to a savings account with 3.26% interest, compounded quarterly. What is the future value of this investment, when Maurice needs to make a down payment?

1)
$23,091.06


2)
$92,364.24


3)
$93,117.01


4)
$23,279.25

Can someone please help me solve this? The answer is number 1, but I don't know how they found it. I keep getting numbers much lower.

Respuesta :

This is an annuity problem. The formula to be used is
FV = P*[ (1+i)^n - 1 ]/i

where,
FV = future value of annuity
P = payment per period
i = interest rate per period
n = number of periods

The annual payment of $3500 is divided into 4 quarters, so 3500/4 = 875 dollar is paid quarterly. This means P = 875

The annual interest rate r = 3.26% = 0.0326 is also divided into 4 parts to get: i = r/4 = 0.0326/4 = 0.00815

There are 24 periods (24 quarters) of payments made because 6 years = (6 years)*(4 quarters/1 year) = 6*4 = 24 quarters. Therefore, n = 24

--------------------------------------

In summary so far, we have

P = 875
i = 0.00815
n = 24

Let's plug those values into the formula to get...

FV = P[(1+i)^n - 1 ]/i
FV = 875[(1+0.00815)^24 - 1 ]/0.00815
FV = 875[(1.00815)^24 - 1 ]/0.00815
FV = 875(1.21507673897319 - 1)/0.00815
FV = 875(0.215076738973192)/0.00815
FV = 875(26.389783923091)
FV = 23091.0609327046
FV = 23091.06

Final Answer: $23,091.06

Otras preguntas