Veronica plans to make a $95 a month annuity payment to an account that earns 3% annual interest to build up her savings. How much can she save in 10 years with this plan?
A. $7,122.49
B. $13,275.43
C. $21,846.27
D. $38,960.76..
I think the answer is D but I'm not very good at this stuff... Please help it's URGENT!!!
Annuities and Retirement Plans Quick Check
1. When you save, you earn interest on your savings and even earn interest on the previous year's interest. What is the name for this type of interest?
Answer: Compound interest
2. What is the name for the type of arranged monthly payment that is made from a savings or retirement fund so that the balance may continue to draw interest?
Answer: Annuity
3. Veronica plans to make $95 a month annuity payment to an account that earns 3% annual interest to build up her savings. How much can she save in 10 years with this plan?
Answer: $13,275.43
Answer is B just did the test
Chad is correct as of 4/15/2022
P [ (1+r)^n -1 ] / r
where P is the annual payment = 95*12 = 1140
r = 0.03
1+r = 1.03
n = 10
so (1+r)^10 = 1.344
-1 = 0.344
so
1140 [ 0.334] / .03 = 13068.82
approximately. I may have carried more or less significant figures
Well, first of all, let me just say that I'm glad I'm not the one responsible for your savings because I'm a clown bot and I tend to spend money on red noses and oversized shoes. But lucky for you, I can still help with this math problem!
To find out how much Veronica can save in 10 years with her annuity payments, we can use the formula for the future value of an ordinary annuity, which is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value (what Veronica will save in 10 years),
P is the monthly payment ($95),
r is the interest rate per period (3% or 0.03),
and n is the number of periods (10 years, which is 120 months).
Now, let's plug in the numbers:
FV = $95 * [(1 + 0.03)^120 - 1] / 0.03
Calculating that out, we find that Veronica can save approximately $21,846.27 (option C). So, grab your money-saving wig and start clowning around with those savings!
To find out how much Veronica can save in 10 years with a $95 monthly annuity payment and a 3% annual interest rate, we can use the formula for the future value of an annuity.
The formula for the future value of an ordinary annuity is:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value of the annuity
P is the monthly payment
r is the interest rate per period
n is the number of periods
In this case:
P = $95
r = 3% = 0.03 (since it's given as an annual rate)
n = 10 years * 12 months/year = 120 months (since we need to convert the number of years to months)
Now, let's substitute the values into the formula and solve for FV:
FV = $95 * [(1 + 0.03)^120 - 1] / 0.03
Using a calculator or spreadsheet, we can calculate the result. After performing the calculations, the answer is option D, $38,960.76.
Therefore, Veronica can save $38,960.76 in 10 years with this savings plan.
Poorly worded question.
To use the formula:
amount = paym( (1+i)^n - 1)/i
the payment period and the interest period MUST be the same
i.e. if the payments are made monthly, then the interest rate must be
compounded monthly
In our question it says that the account earns 3% annual interest. Unless otherwise
stated that implies compounded annually.
to get one of their answers ....
i = .03/12 = .0025
n = 10*12= 120
amount = 95( 1.0025^120 - 1)/.0025 = 13,275.43 <----- one of their answers
correct solution:
We must convert the 3% annual rate to a rate compounded monthly
We have to find the monthly rate i so that
(1+i)^12 = 1.03
1+i = 1.03(1/12) = 1.00246627
So the equivalent monthly rate to an annual rate of 3% is .00246627..
and could be stated as 12(.00246627..) or 2.9595..% per annum, compounded monthly
amount = 95 (1.00246627)^120 - 1)/.00246627 = 13,247.56 , different from theirs by about $28
check:
to show my rate is correct, lets just see what $100 would grow to at
both rates in 1 year:
at 3% per annum: 100(1.03) = $103.00
at 2.95595% per annum compounded monthly = 100(1 + .0295595../12)^12 = $ 103.00