Question

# Lauren plans to deposit \$9000 into a bank account at the beginning of next month and...

Lauren plans to deposit \$9000 into a bank account at the beginning of next month and \$150/month into the same account at the end of that month and at the end of each subsequent month for the next 4 years. 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 years? (Assume she makes no withdrawals during the 4-year period. Round your answer to the nearest cent.)

Deposit Amount at n= 1 is \$9,000

Periodic deposit = \$150

n = 4*12 = 48 months

r = interest rate = 5%/12 = 0.4166667%

Amount in the Account at the end of 4 years = {P * [(1+r)^(n-1) - r] / r} + {\$9,000 * (1+r)^(n-1)}

= {\$150 * [(1+0.4166667%)^(48-1) - 1] /0.4166667%} + {\$9000 * (1+0.4166667%)^(48-1)}

= [\$150 * 0.21582941816 / 0.004166667] + [\$9,000 * 1.21582941816]

= \$7,769.85843233 + \$10,942.4647635

= \$18,712.3231958

Therefore, Amount in account at the end of 4 years is \$18,712.32

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