Question

Suppose on your 21st birthday you begin saving $500 quarterly into an account that pays 12% compounded quarterly. If you continue the savings until your 51st birthday (30 years), how much money will be in the account?

Answer 1

In this case, we have:
P = $500
r = 0.12 (12% as a decimal)
n = 4 (since interest is compounded quarterly)
t = 30 (the number of years)

Plugging in the values, we get:

A = $500(1 + 0.12/4)^(4*30)
A = $500(1 + 0.03)^120
A = $500(1.03)^120
A = $500(15.5919)
A = $7,795.96

Therefore, after 30 years of quarterly savings at a 12% interest rate compounded quarterly, there will be approximately $7,795.96 in the account.

Answer 2

Answer:$386,711.70

Explanation:

To solve the problem, we can use the formula for the future value of an annuity:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value

PMT = payment per period

r = annual interest rate

n = number of compounding periods per year

t = number of years

First, we need to find the number of compounding periods and the interest rate per quarter:

n = 4 (quarterly compounding)

r = 0.12 / 4 = 0.03 (3% quarterly interest rate)

Next, we can plug in the values:

PMT = $500

n = 4

r = 0.03

t = 30

FV = $500 x [(1 + 0.03/4)^(4*30) - 1] / (0.03/4)

FV = $500 x [(1 + 0.0075)^120 - 1] / 0.0075

FV = $500 x [6.3207 - 1] / 0.0075

FV = $500 x 773.4234

FV = $386,711.70

Therefore, if you save $500 quarterly into an account that pays 12% compounded quarterly from your 21st to your 51st birthday, you will have approximately $386,711.70 in the account.