DexterOnline
Junior Member
- Joined
- Jan 29, 2015
- Messages
- 139
Help me find a closed form formula that determines the present value of an annuity that has intermittent gradients. The gradients switch with each term between geometric and arithmetic
The geometric gradient is 10%
The arithmetic gradient is $10
The discount rate is 12% compounded monthly
The geometric gradient is 10%
The arithmetic gradient is $10
The discount rate is 12% compounded monthly
T | PMT | Growth | Discount | PV |
1 | 100 | Geometric | (1.12)^(-1) | 89.29 |
2 | 100 | Arithmetic | (1.12)^(-2) | 79.72 |
3 | 110 | Geometric | (1.12)^(-3) | 78.3 |
4 | 110 | Arithmetic | (1.12)^(-4) | 69.91 |
5 | 121 | Geometric | (1.12)^(-5) | 68.66 |
6 | 120 | Arithmetic | (1.12)^(-6) | 60.8 |
7 | 133.1 | Geometric | (1.12)^(-7) | 60.21 |
8 | 130 | Arithmetic | (1.12)^(-8) | 52.5 |
9 | 146.41 | Geometric | (1.12)^(-9) | 52.8 |
10 | 140 | Arithmetic | (1.12)^(-10) | 45.08 |
11 | 161.051 | Geometric | (1.12)^(-11) | 46.3 |
12 | 150 | Arithmetic | (1.12)^(-12) | 38.5 |
NPV | 742.07 |