Since $110 are deposited monthly, then $110*12 = $1320 are deposited at the end of each year, for the next 6 years in an account paying 4% per year compounded annualy.
To find the value accumulated in increasing annuities you need to take a look at each of the $1320 payment.
Hence, `P = $1320, n = 5, i = 4/100` and the formula used is `A =P(1+i)^n`
The first payment will produce a compound...
Since $110 are deposited monthly, then $110*12 = $1320 are deposited at the end of each year, for the next 6 years in an account paying 4% per year compounded annualy.
To find the value accumulated in increasing annuities you need to take a look at each of the $1320 payment.
Hence, `P = $1320, n = 5, i = 4/100` and the formula used is `A =P(1+i)^n`
The first payment will produce a compound amount of
`1320(1 + 4/100)^5 = 1320*1.04^5`
You need to use n=5 instead n=6 since the money is deposited at the end of the first year and earns interest for only 5 years.
Hence, the future value of annuity is:
`1320*1.04^5 + 1320*1.04^4 + 1320*1.04^3 + 1320*1.04^2 + 1320*1.04^1 + 1320`
Notice that the terms of the sum are the terms of a geometric sequence, having the ratio q = 1.04 and the first term b = 1320.
`S = b*(q^n-1)/(q-1)`
`S = 1320*(1.04^6 -1)/(1.04 - 1)`
`S = 1320*(0.265319018496)/(0.04)`
`S ~~ $8755.527`
Hence, evaluating the amount accumulated in the increasing annuities yields `S ~~ $8755.527.`
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