Question

5. A periodic deposit is made into an annuity with the given terms. Find how much should be regularly deposited in order to have the specified final amount in the account. Round your answer to the nearest dollar.Future value:$215,000Interest rate:4.6%FrequencyquarterlyTime:23 yearsRegular deposit amount: $

Answer 1

Regular deposit amount = $160

Step-by-step explanation

The future value annuity formula is given by

P = PMT x [(1 + r)ⁿ - 1]/r

Where P = Future value

PMT = Regular deposit amount

n = Number of periods in which payments will be made

r = Interest rate

PMT = ?

P = $215000,

r = 4.6% = 4.6/100 = 0.046

n = 4 x 23 = 92

⇒ 215000 = P x [(1 + 0.046)⁹² - 1]/0.046

215000 = P x [(1.046)⁹² - 1]/0.046

215000 x 0.046 = P x [(1.046)⁹² - 1]

9890 = P x [62.65 -1]

61.65P = 9890

P = 9890/61.65

P = $160.42

To the nearest dollar, we have

P = $160