Business, 26.10.2020 16:40 lilquongohard

Suppose that you make a sequence of 31 equal monthly deposits into an account paying a nominal rate of 6.7% convertible quarterly. If the balance in the account 7 months after the final deposit is $8, 000, how large is each deposit

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Answer from: MZ2017

Each Deposit is $228.2

Explanation:

First we need to calculate the effective Interest rate

Effective annual interest rate = [ 1 + APR/n ]^n - 1

Where

APR = 6.7%

n = months ina quarter = 4 months

Placing values in the formula

Effective annual interest rate = [ 1 + 6.7%/4 ]^4 - 1

Effective annual interest rate = 6.87%

Now calculate the monthly effective rate using following formula

Effective monthly rate = [ 1 + Effective annual interest rate ]^(1/n) - 1

Where

n = Months in a year = 12 years

Placing values in the formula

Effective monthly rate = [ 1 + 6.87% ]^(1/12) - 1

Effective monthly rate = 0.55523%

Use following formula to calculate the amount of each deposit

Balance after 7 months of last deposit = Future value of annuity x ( 1 + r )^7

Balance after 7 months of last deposit = [ Monthly deposit x ( 1 + r )^n - 1 / r ] x ( 1 + r )^7

where

Balance after 7 months of last deposit = $8,000

r = 0.55523%

n = 31 months

Placing values in the formula

$8,000 = [ Monthly deposit x ( 1 + 0.55523% )^31 - 1 / 0.55523% ] x ( 1 + 0.55523% )^7

$8,000 = [ Monthly deposit x 33.726 ] x 1.03952

$8,000 / 1.03952 = Monthly deposit x 33.726

$7,695.86 = Monthly deposit x 33.726

Monthly deposit = $7,695.86 / 33.726

Monthly deposit = $228.19

Answer from: Quest

the specific actions take by the fed. what the fed was attempting to do by taking these actions. the result of the actions taken by the fed

Answer from: Quest

1) the stages a new product goes through from beginning to end, i.e., the stages that a product passes through from introduction through growth, maturity, and decline. 2) the time from initial research and development to the time at which sales and support of the product to customers are withdrawn. 3) the period of time during which a product can be produced and marketed profitably.

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