1. Find Time n = ?
Present value C = 1000, Interest Rate i = 10%, Future value FV = 1331,
Interest compounded = Year (1/year)
for Present value using Compound Interest method

Solution:
`C=1000`

`i=10%=0.1` per year (Interest rate)

`FV=1331` (Future value)

Now, Future value (Compound Interest) formula is
`FV=C*(1+i)^n`

`:.1331=1000*(1+0.1)^n`

`:.(1331)/(1000)=(1.1)^n`

`:.1.33=(1.1)^n`

`:.1.1^n=1.33`

taking natural log on both the sides
`:.ln(1.1^n)=ln(1.33)`

`:.n*ln(1.1)=ln(1.33)`

`:.n=ln(1.33)/ln(1.1)`

`:.n=(0.29)/(0.1)`

`:.n=3` year

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2. Find Time n = ?
Present value C = 5000, Interest Rate i = 10%, Future value FV = 6050,
Interest compounded = Year (1/year)
for Present value using Compound Interest method

Solution:
`C=5000`

`i=10%=0.1` per year (Interest rate)

`FV=6050` (Future value)

Now, Future value (Compound Interest) formula is
`FV=C*(1+i)^n`

`:.6050=5000*(1+0.1)^n`

`:.(6050)/(5000)=(1.1)^n`

`:.1.21=(1.1)^n`

`:.1.1^n=1.21`

taking natural log on both the sides
`:.ln(1.1^n)=ln(1.21)`

`:.n*ln(1.1)=ln(1.21)`

`:.n=ln(1.21)/ln(1.1)`

`:.n=(0.19)/(0.1)`

`:.n=2` year

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