1. Suppose Mary deposits $200 at the end of each month for 30 years into an account that pays 5% interest compounded monthly.
a. How much total money will she have in the account at the end?
b. How much total money did Mary actually deposit?
c. How much total interest did the account earn over that period?
d. Suppose instead of making monthly deposits, Mary decides to deposit a “lump sum” into the account. How much must she deposit? What is this value also called?
This question and the question in your previous post suggest that you are studying compound interest.
Both are very routine questions that you should be able to answer quite readily.
Payment=200
i = .05/12 = .004166667
n = 30(12) = 360
a)
amount = 200(1.004166667^360 - 1)/.004166667 = 166451.75
b) and c) --- very easy
d)
166451.75 = PV(1.004166667)^360 , where PV is present value . or your "lump sum"
= 37256.33
I don't understand
a. To calculate the total money Mary will have in the account at the end, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account
P = the principal amount (the initial deposit), which in this case is $200
r = the annual interest rate (converted to decimal form), which is 5% or 0.05
n = the number of times interest is compounded per year, which is monthly, so n = 12
t = the number of years Mary will be depositing money, which is 30
Plugging in the values, we get:
A = 200(1 + 0.05/12)^(12*30)
Calculating this expression will give us the total amount of money in the account at the end.
b. To find the total amount of money Mary actually deposited, we can simply multiply the amount she deposited each month by the number of months in 30 years.
Total Deposits = Deposit per Month * Months
Total Deposits = $200 * 12 * 30
This will give us the total amount of money Mary deposited into the account.
c. To calculate the total interest earned by the account over the 30-year period, we can subtract the total deposits from the total amount of money in the account.
Total Interest = Total Amount - Total Deposits
d. If Mary decides to deposit a "lump sum" instead of making monthly deposits, the amount she must deposit can be found using the formula for future value of a lump sum:
A = P(1 + r/n)^(nt)
Where:
A = the total desired amount, which is the same as the one calculated in part a
P = the principal amount, or the lump sum that Mary needs to deposit
r = the annual interest rate (converted to decimal form), which is 5% or 0.05
n = the number of times interest is compounded per year, which is monthly, so n = 12
t = the number of years Mary will deposit the lump sum, which is 30
By plugging in the values and solving for P, we can find the amount Mary needs to deposit as a lump sum. Additionally, this value is also called the future value of the lump sum.