Question

Lauren plans to deposit $3000 into a bank account at the beginning of next month and $250/month into the same account at the end of that month and at the end of each subsequent month for the next 4 yr. If her bank pays interest at a rate of 5%/year compounded monthly, how much will Lauren have in her account at the end of 4 yr? (Assume she makes no withdrawals during the 4-yr period.  Round your answer to the nearest cent.)
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Answer 1

The formula for compound interest is F = P(1+r)ⁿ , where P is the principal/initial deposit, r is the rate of interest ,n is the number of years and F is the maturity value. Here, P = $ 3000, r = 5/1200 = 1/240 and n = 12*4 =48. Then F = 3000(1+1/240)⁴⁸ = 3000*1.220895355 = $ 3662.69 ( on rounding off to the nearest cent).

The formula for the future value (F) of an annuity is F =( P/r)[(1+r)ⁿ -1] where P is the periodic payment, r is the rate of interest for the period and n is the number of periods. Here, P = $ 250, r = 5/1200 = 1/240, n = 12*4 -1 = 47 so that F = [250/(1/240)][(1+1/240 )⁴⁷ -1] = 60000*1.215829399 = $ 72949.76( on rounding off to the nearest cent). Additionally, there is another $ 250 deposited at the end of the 48^th month. Hence Lauren will have $ 3662.69 +$ 72949.76+$ 250 = $ 76862.45 in her account at the end of 4 years.