Find the amount accumulated in the increasing annuities. $110 deposited monthly for 6 years at 4 % per year. ( Assume the end of period deposits and compounding at the same intervals as deposits).

Expert Answers
sciencesolve eNotes educator| Certified Educator

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.`