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
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!!!
5 answers
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
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
Answer is B just did the test
Chad is correct as of 4/15/2022
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
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
1 answer