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An amount of $8000 is invested for a period of 4 years.
The interest rate for this investment is 7.2% per annum compounding quarterly.
The interest earned by the investment in the fourth year (in dollars) is given by
`C`
`text{Interest earned in 4th year}\ = FV\text{(after 4 years)}-FV\text{(after 3 years)}`
`text{Interest rate}\ (r) = \frac{7.2%}{4} = \frac{0.072}{4} = 0.018`
`text{Compounding periods (3 years)}\ = 3 xx 4 = 12`
`text{Compounding periods (4 years)}\ = 4 xx 4 = 16`
`FV\text{(after 4 years)}\ = PV(1+r)^n = 8000(1.018)^16`
`FV\text{(after 3 years)}\ = 8000(1.018)^12`
`:.\ text(Interest earned in 4th year) = 8000 xx 1.018^(16)-8000 xx 1.018^(12)`
`=> C`