SOLUTION: The question is: Hannah invests $4500 in an investment with an APR of 5.2% compounded monthly. She also makes a monthly deposit of $200 per month into this same investment. What i

Question 1084563: The question is:
Hannah invests $4500 in an investment with an APR of 5.2% compounded monthly. She also makes a monthly deposit of $200 per month into this same investment. What is the total amount of money in this investment after 3 years?
I tried the savings formula: 4500 * ((1+(.052/12)^(3*12)-1) / (.052/12)
which didn't have anywhere to fit the $200 in, and also got me 0 as an answer. What formula should I use?
Found 3 solutions by Fombitz, Boreal, MathTherapy:
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
Use the future value of an annuity formula,

where P is the monthly payment, r is the monthly rate, and n is the number of periods.
In this case,

So the first and each monthly payment is $200. Since the real first payment is $4500, you also have to add $4300 compounded similarly for the same time period to the total you get to make up for this.
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
4500* ((1+(.052/12)^(36)) + 200(1+.052)^36-1)/(0.052/12). The 200 goes into a separate term. Essentially, what you are doing is figuring the ongoing value of the original $4500 and then adding to it the amount you are contributing each month as well. The 4500 is the compound interest formula, and that is just added to the periodic deposit formula.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The question is:
Hannah invests $4500 in an investment with an APR of 5.2% compounded monthly. She also makes a monthly deposit of $200 per month into this same investment. What is the total amount of money in this investment after 3 years?
I tried the savings formula: 4500 * ((1+(.052/12)^(3*12)-1) / (.052/12)
which didn't have anywhere to fit the $200 in, and also got me 0 as an answer. What formula should I use?

Use the FUTURE VALUE of $1 FORMULA, or: for the $4,500 lump-sum, where:
= Future value of the ACCUMULATED amount in the account after "t" years
= Principal or original amount invested
= Annual interest rate
= Number of compounding periods, per annum
= Time, in years amount is invested
Use the **FUTURE VALUE of an ORDINARY ANNUITY FORMULA, or: for the $200 monthly payment/deposit, where:
= Future value of the $200 monthly payments/deposits after "t" years
= Payment/Deposit per period
= Annual interest rate
= Number of compounding periods, per annum
= Time, in years amount is invested
** You already know and have used this formula, but the 4,500 s/b 200.

Add the 2 and you should have the total amount in the account after 3 years. Hint: (Total amount s/b: $$13,031.75).
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