Present and Accumulated Values of an Annuity-Immediate

Problem 15.1 Consider an investment of $5,000 at 6% convertible semiannually. How much can be withdrawn each half−year to use up the fund exactly at the end of 20 years? Solution. 5,000 = Xa_{\overline{40|}0.03} \\ \implies X = 216.31 Problem 15.2 The annual payment on a house is$18,000. If payments are made for 40 years, how much is the house worth assuming annual interest rate of 6%? Solution....

Equations of Value and Time Diagram

Problem 12.1 In return for payments of $5,000 at the end of 3 years and$4,000 at the end of 9 years, an investor agrees to pay $1500 immediately and to make an additional payment at the end of 2 years. Find the amount of the additional payment if i^{(4)} = 0.08. Solution. 5,000(1 + \frac{0.08}{4})^{-3 \times 4} + 4,000(1 + \frac{0.08}{4})^{-9 \times 4} \\ = 1,500 + X(1 + \frac{0.08}{4})^{-2...

Solving for Unknown Time

Problem 14.1 The present value of a payment of $5,000 to be made in t years is equal to the present value of a payment of$7,100 to be made in 2t years. If i = 7.5\% find $t4. Solution. 5,000(1+0.075)^{-t} = 7,100(1+0.075)^{-2t} \\ \implies 5,000 = 7,100(1 + 0.075)^{-t} \\ \implies t = 4.84...

Solving for the Unknown Interest Rate

Problem 12.1 In return for payments of $5,000 at the end of 3 years and$4,000 at the end of 9 years, an investor agrees to pay $1500 immediately and to make an additional payment at the end of 2 years. Find the amount of the additional payment if i^{(4)} = 0.08. Solution. 5,000(1 + \frac{0.08}{4})^{-3 \times 4} + 4,000(1 + \frac{0.08}{4})^{-9 \times 4} \\ = 1,500 + X(1 + \frac{0.08}{4})^{-2...

HTML, CSS - Center Vertically (SLIDE MENU)

HTML: CSS: div.container { position: relative ; width: 250px; height: 250px; background-color: green; } div.left { margin: 0; background: black; opacity: 0.65; position: absolute; top: 50%; transform: translate(-0%, -50%); height: 61px; width: 38px; left: 0px; } div.right { margin: 0; background: black; opacity: 0.65; ...

Swift Request for Authorization

* Photos func requestForAccessPhotos(view : UIViewController, completionHandler: (accessGranted: Bool) -> Void){ let authorizationStatus = PHPhotoLibrary.authorizationStatus() switch authorizationStatus { case .Authorized: completionHandler(accessGranted: true) case .Denied, .NotDetermined: PHPhotoLibrary.requestAuthorization() {(status)...

Swift Infix Custom Threading

Code: func ~> (task: ()->Void, update: ()-> Void) { let priority = DISPATCH_QUEUE_PRIORITY_DEFAULT dispatch_async(dispatch_get_global_queue(priority, 0)) { // do some task task() dispatch_async(dispatch_get_main_queue()) { // update some UI update() } } } Usage: ({ for i in 0..<100000{ print("count:...