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anonymous
 5 years ago
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?
anonymous
 5 years ago
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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radar
 5 years ago
Best ResponseYou've already chosen the best response.0I 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

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I 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.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Do you have a reference that deals with a annual or periodic deposit with compounded interest?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Future Value Future Value (FV) refers to the amount of cash to be received or paid at a future date. Singleperiod 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 Multiperiod 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 15year 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 builtin 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.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0would I use a single period, or the multi period formula?

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I 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.

radar
 5 years ago
Best ResponseYou've already chosen the best response.0Maybe an excel spreadsheet........

radar
 5 years ago
Best ResponseYou've already chosen the best response.0I put it on a spreadsheet and it appears that Julian has $17,859.63 enough to buy a big rock!

radar
 5 years ago
Best ResponseYou've already chosen the best response.0It is an open office spreadsheet.
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