Julian has been secretly depositing $500 in his savings account (earning five percent) every Christmas starting when he was 16 years old. Next year, he wants to surprise his girlfriend with a diamond ring for Christmas. Julian will be 36 and has finally found a girlfriend of which his mother approves. Julian’s savings account is compounded annually. How much will Julian be able to spend on the ring after his $500 contribution this year?

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Julian has been secretly depositing $500 in his savings account (earning five percent) every Christmas starting when he was 16 years old. Next year, he wants to surprise his girlfriend with a diamond ring for Christmas. Julian will be 36 and has finally found a girlfriend of which his mother approves. Julian’s savings account is compounded annually. How much will Julian be able to spend on the ring after his $500 contribution this year?

Mathematics
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I just looked up the compound interest formula and it is:\[A=P(1+r/n)^{nt}\] Where A is the amount saved including interest earned P is the amount of deposit r is the interest rate n is the number of times interest is calculated per year. t is the period of time
I am beginning to think this formula would only solve for the initial deposit and somehow we have to consider his annual deposit of $500 for the 20 year period.
Do you have a reference that deals with a annual or periodic deposit with compounded interest?

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Other answers:

Future Value Future Value (FV) refers to the amount of cash to be received or paid at a future date. Single-period Potential investments offer a rate of return of 9% per period. Given an initial investment of $2,000 how much cash would be available at the end of one period? The investment will return the principal $2,000 plus 9% of $2,000 or $2,180 which is calculated as follows: FV = (1,000 + 1,000 * 0.09) = 1,000 (1 + .09) = 1,000 (1.09) = 1,090 The FV for one period is: FV = initial investment * (1 + interest rate) The equation is: FV = PV (1 + r) where, FV = Future value PV = Present value r = Periodic rate of return Multi-period To continue with the above example what will the investment be worth after four periods assuming that the accrued amount can be reinvested at a rate of 9%? FV = 1,000 * 1.09 * 1.09 * 1.09 * 1.09 = 1,090 * 1.09 * 1.09 * 1.09 = 1188.10* 1.09 * 1.09 = 1295.03 * 1.09 = 1411.58 After four periods the value of the investment will be $1411.58. Although the above method correctly calculates the future value, it is inefficient because you need to multiply $1,000 with 1.09 four times. What if the investment was for 50 periods instead of 4? We can simplify the equation by using exponents, as shown: FV = 1,000 * (1.09)4 = 1,000 * (1.41158) = 1411.58 To calculate the FV for multiple periods, the equation is given by: FV = initial investment * (1 + interest rate) time or FV = PV (1 + r) n where, n = number of periods Example: Albert plans to retire in 15 years. Will he be able to afford a $200,000 condominium when he retires if he invests $100,000 in a 15-year certificate of deposit (CD) that pays 6% interest, compounded annually? Solution: Yes, he will be able to purchase the condominium because he should have $100,000 (1.06)15 = 239,655.82 when he retires. You can solve this problem in several ways: Using the formula and a scientific calculator Using a financial calculator Using an Excel spreadsheet Using a financial calculator: Input: PV = $100,000 I = 6 N = 15 PMT = 0 Compute: FV = $239,655.82 Note: Financial calculators use built-in sign conventions. So the answer may be $239,655.82. Cash inflows are represented by a plus sign and cash outflows are represented by a minus sign. Albert invests $100,000 in the CD, and this is a cash outflow. The result will be a positive value because Albert will receive that amount.
would I use a single period, or the multi period formula?
I think they are discussing periods for the calculation of interest (for example quarterly vs annually) It is not considering the muulti deposit of principal. I need to do some research. Now I got to run. sorry I couldn't help.
Maybe an excel spreadsheet........
I put it on a spreadsheet and it appears that Julian has $17,859.63 enough to buy a big rock!
Here is spread sheet
1 Attachment
It is an open office spreadsheet.

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