Question

You would like to have $170,000 in 12 years by making regular deposits at the end of each month in an annuity that pays 8.25% compounded monthly. How much of the $170,000 comes from interest? Round your answer to the nearest dollar.

Answer 1

The first thing needed to be done is to find out the monthly payment

Answer 2

so we use this formula

P = FV( r/n )/((1+r/n)^(n*t) - 1 )

Answer 3

P = monthly payment
FV = future value
r = annual interest rate
n = compounding frequency
t = # of years

Answer 4

in this case

P = unknown
FV = 170000
r = 0.0825
n = 12
t = 12

Answer 5

so plug all this in to get


P = FV( r/n )/((1+r/n)^(n*t) - 1 )


P = 170000( 0.0825/12 )/((1+0.0825/12)^(12*12) - 1 )


P = 694.802351688371


P = 694.80

Answer 6

so the monthly payment is $694.80

with me so far?

Answer 7

yes. theres more to it?

Answer 8

yes

Answer 9

you make deposits of $694.80 at the end of each month for 12*12 = 144 months

Answer 10

so in total, you deposit 144*694.80 = 100,051.20 dollars over 12 years

Answer 11

you deposit a total of 100,051.20 dollars

but after 12 years, you will have $170,000 in the account

so the difference is from the interest made

Answer 12

170,000 - 100,051.20 = 69,948.80

So you made 69,948.80 dollars in interest

Answer 13

Thank you so much! THis really helped

Answer 14

glad it did

Answer 15

I have another question!

Answer 16

whats that

Answer 17

You deposit $100 into a savings plan at the end of each year. The interest rate is 6% compounded annually. Find the value of the annuity after 7 years. Do not round until the final answer. Then, round to the nearest cent

Answer 18

what you want is the future value (FV) of the annuity

Answer 19

so you use this formula

FV = P((1+r/n)^(n*t) - 1 )/( r/n )

in this case

P = 100
r = 0.06
n = 1
t = 7

Answer 20

I'll let you compute it. Tell me what you get.

Answer 21

236.42?

Answer 22

or is it 839.38?

Answer 23

one sec

Answer 24

FV = P((1+r/n)^(n*t) - 1 )/( r/n )


FV = 100((1+0.06/1)^(1*7) - 1 )/( 0.06/1 )


FV = 839.383764985601


FV = 839.38

Answer 25

so that's how much will be in the account after 7 years

Answer 26

Extra info: you made 7 payments of $100 each, so you put in 7*100 = 700 dollars total

Interest Made: 839.38 - 700 = 139.38 dollars

Answer 27

Thank you so much!

Answer 28

np