Question

Nick can invest $10,000 in either one of two annuities. Annuity A has a 6% annual interest rate and requires a starting principal of $9,000, plus annual $100 deposits for the next 10 years. Annuity B has a 12% annual interest rate and requires a starting principal of $9,000, plus annual $200 deposits for the next 5 years.

Answer 1

Let's start by cutting it into parts.
What we're doing with this equation is finding both values of annuities A and B and subtracting them. Let's begin with annuity A.

First, take your numbers out of the word problem:
$10,000 for investment
6% annual interest rate
$9,000 starting principal
$100 deposits annually for 10 years

Answer 2

ok got that, whats thr right formula to find out the final. i thought i found one but idk where the investment part goes in the equation

Answer 3

PV = P x (1 - (1 + r ) ^- n) / r


PV = present value of an ordinary annuity
P = value of each payment
r = interest rate per period
n = number of periods

Answer 4

ok i tried that one before and got 91.333... which isnt possible

Answer 5

how did you substitute into the equation?

Answer 6

100 x (1 - (1+6)^-10) /6 = 99.999999941

Answer 7

it just got even more confusing
idk where the 9,000 or the 10,000 goes

Answer 8

Cheese it, im guessing
this is way too confuisng and im just waisting your time at this point

Answer 9

thx for the help tho

Answer 10

nono, hold on

Answer 11

PV would be the 9,000 because it is the initial deposit

Answer 12

ok still not understanding it unforuetly

Answer 13

i just realized

Answer 14

what

Answer 15

i feel so dumb. $9000 is the principal sort of like the down payment, so we go ahead and take it off of the $10000, leaving us with $1000 with 10 years of $100 annual payments and a 6%, or .06 rate of return and now we can calculate

Answer 16

PV = P x (1 - (1 + r ) ^- n) / r, right?

so if
PV = present value of an ordinary annuity
P = value of each payment
r = interest rate per period
n = number of periods

$1000 = 100 x (1 - (1 + 6%)^-10) / 6%

Answer 17

yee that makes more sense

Answer 18

i'm sorry! i feel so slow rn

Answer 19

lol its fine, i guessed and still made it out with a good grade. if its night there you should go sleep lol

Answer 20

nO i wAnT tO sOLvE!! sleep is for casuals