In June of 2015, you begin depositing $300 per month into an annuity.(a) If the interest...

In June of 2015, you begin depositing $300 per month into an annuity.(a) If the interest rate is 1.4% compounded monthly, determine the value of the account in June 2016.(b) In June 2016, the interest rate increases to 2.2% compounded monthly, determine the value of theaccount in June 2017.

Solutions

Expert Solution

We are required to calculate the future value of an annuity for which formula is:

a) Therefore, P = $ 300, r= 1.4/100 = 0.014, n = 11 (assuming that the investment is done at the end of the month)

Applying values given in question, we get,

FV i.e. Future Value = 300 [ (1+0.014)¹¹ - 1] / 0.014

= 300 * [1.1816 - 1]/0.014

= 300 * [0.1816/0.014]

= 300 * 12.9714

= $ 3891.42

Value of Account in June, 2016 = $ 3891.42

b) P = $ 300, r= 2.2/100 = 0.022, n = 11 (assuming that the investment is done at the end of the month)

Applying values given in question, we get,

FV i.e. Future Value = 300 [ (1+0.022)¹¹ - 1] / 0.022

= 300 * [1.2984 - 1]/0.022

= 300 * [0.2984/0.022]

= 300 * 13.5636

= $ 4069.08

Value of Account in June, 2017 = $ 4069.08

The question is to answer value of Account in June, 2017, if it is assumed that, total value of account is asked in the question , we would add to it the value as in June, 2016, therefore,

resulting value in June, 2017 = $ 3891.42 + $ 4069.08

= $ 7960.5

ekkarill92 answered 1 year ago

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