helpppppppp

[Guest]

How do you do this question:

Cora recieved an insurance settlement of $80000, which she invested at 5.2% per annum, compounded monthly, to provide a payment each month for 10 years, starting next month.

a) How much will each payment be?
b) How much did Cora's insurance settlement give her altogether?


Here's also a similar question I think...well I don't get it:

A lottery to raise funds for a hospital is advertising a $240 000 prize. The winner will recieve $1 000 every month for 20 years, starting a year from now.

a) If the interest rate is 8.9% per annum, compounded anually, how much must be invested now to have the money to pay this prize?
b) If the lottery were able to negotiate an interest rate of 9.3% per annum compounded annually, how much would be invested now?

Thanks for the help,
Anna

 

[Denis]

How do you do this question:
Cora recieved an insurance settlement of $80000, which she invested at 5.2% per annum, compounded monthly, to provide a payment each month for 10 years, starting next month.
a) How much will each payment be?
Thanks for the help, Anna

p = ai / (1 - x) where x = 1 / (1 + i)^n
p = payment : ?
a = amount : 80000
i = interest per month : .052/12
n = number of months : 12*10

good luck with the rest...I'm watching Steve Nash...

 

[soroban]

Hello, Anna!

Cora recieved an insurance settlement of $80000,
which she invested at 5.2% per annum, compounded monthly,
to provide a payment each month for 10 years, starting next month.

a) How much will each payment be?
b) How much did Cora's insurance settlement give her altogether?

They often give this problem different names, like "Sinking Fund".
I used to find it confusing until I saw through it.

This is basically an <u>Amortization</u> problem.
It is as if Cora loaned the company $80,000 at a 5.2% annual rate
. . and they are repaying her in 120 monthly payments.

. . . . . . . . . . . . . . . . . . . . . .i(1 + i)ⁿ
The formula is: . A . = . P --------------
. . . . . . . . . . . . . . . . . . . . (1 + i)ⁿ - 1

where: . P = principal
. . . . . . . .i = periodic interest rate
. . . . . . . n = number of periods
. . . . . . . A = periodic payment

. . . . . . . . . . . . . . . . . . . . .(0.052/12)(1 + 0.052/12)¹²⁰
We have: . A . = . 80,000 ------------------------------------- . = . $856.37 per month (a)
. . . . . . . . . . . . . . . . . . . . . . . (1 + 0.052/12)¹²⁰ - 1

She will receive a total of: . 120 x $856.37 .= .$102,764.40 (b)

 

[Denis]

How do you do this question:
Cora recieved an insurance settlement of $80000, which she invested at 5.2% per annum, compounded monthly, to provide a payment each month for 10 years, starting next month.
a) How much will each payment be?

This is same as a loan of $80000 over 120 months (10 * 12), the interest
being .052/12 each month: what's the monthly payment?
p = ai / (1 - x) where x = 1 / (1 + i)^n; so:
p = 80000(.052/12) / [1 - 1 / (1 + .052/12)^120]
that'll work out to be 856.3663...

b) How much did Cora's insurance settlement give her altogether?

That's an unclear question: probably means "monthly payment * 120".


Here's also a similar question I think...well I don't get it:
A lottery to raise funds for a hospital is advertising a $240 000 prize. The winner will recieve $1 000 every month for 20 years, starting a year from now.
a) If the interest rate is 8.9% per annum, compounded anually, how much must be invested now to have the money to pay this prize?
b) If the lottery were able to negotiate an interest rate of 9.3% per annum compounded annually, how much would be invested now?

I'm not gone to spend a lot of time here: you should learn the easy ones
first...which you still don't seem to understand...
Anyway, the "$240,000" makes no sense, since the winner gets $1000
per month for 20 years

It'll work like this:
1: $a is invested now
2: interest at 8.9% will be paid in 1 year: so value will be a(1 + .089)
3: beginning in year#2, $1000 is withdrawn each month from that amount
4: the interest rate must be adjusted to a rate which, when compounded
monthly, will be the equivalent of 8.9% compounded annually...NO, I'm
not showing you how! ...yet...

I suggest you make sure of the interest rate's compounding frequency
(ask your teacher); seems a bit early for you to get involved in
complicated rate conversions...