Exponential Functions

Continuous Compounding

\[ FV = PVe^{rt}\]

FV <- function(t) {
  100*exp(0.05*t)
}

t <- seq(from=0,to=30,by=1)

plot(FV(t)~t,type="l")

# Value of Money at t = 20

FV(20)
## [1] 271.8282
FV_30 <- FV(t)

FV_30[21]
## [1] 271.8282

Data Frames

t <- seq(from=0,to=40,by=1)

PV <- 100
r <- 0.05

# Cont. Compounding

FV <- PV*exp(r*t)

RATIO <- FV/PV

lnRATIO <- log(RATIO)

dat <- data.frame(t,FV,RATIO,lnRATIO)

dat
##     t       FV    RATIO lnRATIO
## 1   0 100.0000 1.000000    0.00
## 2   1 105.1271 1.051271    0.05
## 3   2 110.5171 1.105171    0.10
## 4   3 116.1834 1.161834    0.15
## 5   4 122.1403 1.221403    0.20
## 6   5 128.4025 1.284025    0.25
## 7   6 134.9859 1.349859    0.30
## 8   7 141.9068 1.419068    0.35
## 9   8 149.1825 1.491825    0.40
## 10  9 156.8312 1.568312    0.45
## 11 10 164.8721 1.648721    0.50
## 12 11 173.3253 1.733253    0.55
## 13 12 182.2119 1.822119    0.60
## 14 13 191.5541 1.915541    0.65
## 15 14 201.3753 2.013753    0.70
## 16 15 211.7000 2.117000    0.75
## 17 16 222.5541 2.225541    0.80
## 18 17 233.9647 2.339647    0.85
## 19 18 245.9603 2.459603    0.90
## 20 19 258.5710 2.585710    0.95
## 21 20 271.8282 2.718282    1.00
## 22 21 285.7651 2.857651    1.05
## 23 22 300.4166 3.004166    1.10
## 24 23 315.8193 3.158193    1.15
## 25 24 332.0117 3.320117    1.20
## 26 25 349.0343 3.490343    1.25
## 27 26 366.9297 3.669297    1.30
## 28 27 385.7426 3.857426    1.35
## 29 28 405.5200 4.055200    1.40
## 30 29 426.3115 4.263115    1.45
## 31 30 448.1689 4.481689    1.50
## 32 31 471.1470 4.711470    1.55
## 33 32 495.3032 4.953032    1.60
## 34 33 520.6980 5.206980    1.65
## 35 34 547.3947 5.473947    1.70
## 36 35 575.4603 5.754603    1.75
## 37 36 604.9647 6.049647    1.80
## 38 37 635.9820 6.359820    1.85
## 39 38 668.5894 6.685894    1.90
## 40 39 702.8688 7.028688    1.95
## 41 40 738.9056 7.389056    2.00