1. Find Interest Rate i = ?
Principal P = 1000, Time n = 5 Year, Future value FV = 1649,
for Contineous Compounding method

Solution:
`P=1000`

`n=5` years (Number of periods)

`FV=1649` (Future value)

`FV=P*e^(i*n)`

`:.1649=1000*e^(i*5)`

`:.1649/1000=e^(i*5)`

`e^(i*5)=1.65`

taking natural log on both the sides
`:.ln(e^(i*5))=ln(1.65)`

`:.i*5=0.5`

`:.i=0.5/5`

`:.i=0.1`

`:.i=10 %` per year

Year	Principal	Yearly Interest	Total Interest	Total Balance
0	1000	0	0	1000
1	1000	105.21	105.21	1105.21
2	1000	116.28	221.49	1221.49
3	1000	128.51	350	1350
4	1000	142.03	492.03	1492.03
5	1000	156.97	649	1649

---

2. Find Interest Rate i = ?
Principal P = 5000, Time n = 3 Year, Future value FV = 6749,
for Contineous Compounding method

Solution:
`P=5000`

`n=3` years (Number of periods)

`FV=6749` (Future value)

`FV=P*e^(i*n)`

`:.6749=5000*e^(i*3)`

`:.6749/5000=e^(i*3)`

`e^(i*3)=1.35`

taking natural log on both the sides
`:.ln(e^(i*3))=ln(1.35)`

`:.i*3=0.3`

`:.i=0.3/3`

`:.i=0.1`

`:.i=10 %` per year

Year	Principal	Yearly Interest	Total Interest	Total Balance
0	5000	0	0	5000
1	5000	525.77	525.77	5525.77
2	5000	581.06	1106.84	6106.84
3	5000	642.16	1749	6749

---