# Business & Economics Applications of Growth / Decay Models Integration

##### 251 words — categories: calculus

```
from math import e
def pv(p, k, t):
k = k / 100
return p * e**(-k*t)
def fv(p, k, t):
k = k / 100
return p * e**(k*t)
def apv(r, k, t):
k = k / 100
return (r / k) * (1 - e**(-k*t))
def afv(r, k, t):
k = k / 100
return (r / k) * (e**(k*t) - 1)
```

## Present Value of a Trust

In 18 years, Maggie Oaks is to receive $200,000 under the terms of a trust established by her grandparents. Assuming an interest rate of 5.8%, comopounded continuously, what is the present value of Maggie’s legacy?

`pv(200000, 5.8, 18)`

`## 70408.73742039692`

## Salary Value

At age 35, Rochelle earns her MBA and accepts a position as vice president of a company. Assume she will retire at the age of 65, having received an annual salary of $95,000 and the that interest rate is 6% compounded continuously.

- What is the present valye of her position?
- What is the accumulated future value of her position?

```
years = 65 - 35
apv(95000, 6, years)
```

`## 1321610.0936491548`

`afv(95000, 6, years)`

`## 7995275.151987163`

## Early Retirement

Lauren Johnson signs a 10-yr contract as a loan office for a bank, at a salary of $84,000 per year. After 7 yr, the bank offers her early retirement. What is the least amount the bank should offer Lauren, given that the going interest rate is 7.4%, compounded continuously?

```
total_comp = afv(84000, 7.4, 10)
earned_comp = afv(84000, 7.4, 7)
total_comp - earned_comp
```

`## 473656.2012921268`