Answer to Question #93631 in Financial Math for Atiyya

Question

$100 is deposited at the beginning of every week for five years in an account that pays 14%/a, compounded weekly.
What type of annuity is this?
Find the future value of the annuity using the formula.
Find the future value of the annuity using a spreadsheet. In your answer include the formulas that you typed.
Find the future value of the annuity using the TVM solver on a graphing calculator or on a website. In your answer, include what values you typed for each parameter.

Answer 1

What type of annuity is this?

Annuities whose payments are made at the end of the period are "ordinary annuity" type

Find the future value of the annuity using the formula.

Future value of an ordinary annuity:

A = accumulated amount

pymnt = period payments = 100

r = rate = 14 % = 14 / 100 = 0.14

n = times it compounds per year weekly, thus - 52

t = years = 5

	A = 100 * ((1+0.14/52)^52*5 - 1) / (0.14/52)= 37,583.35

Find the future value of the annuity using a spreadsheet. In your answer include the formulas that you typed.

=FV(B3;B4;-B2;;0)

Find the future value of the annuity using the TVM solver on a graphing calculator or on a website. In your answer, include what values you typed for each parameter.

Input values:

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Periodic payment amount PMT = 100

Nominal interest rate R = 14% per year

Compounding period N = weekly = 52 times per year

Time period T = 5.0 years * 1 = 5 years

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Calculated values:

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Future value FV = PMT * ((1 + (R / N)) ^ (N * T) - 1) / (R / N) = 100 * ((1 + (0.14 / 52)) ^ (52 * 5) - 1) / (0.14 / 52) = 37583.35

Interest I = FV - N * T * PMT = 37583.35 - 52 * 5 * 100 = 11583.35

Effective Interest rate Re = (((1 + (R / N)) ^ N) - 1) * 100% = (((1 + (0.14 / 52)) ^ 52) - 1) * 100% = 15.01%

Interest rate per period r = R / N * 100% = 0.14 / 52 * 100% = 0.27%