How much will you have in a savings account in ten years, if you deposit $1,600

Question

How much will you have in a savings account in ten years, if you deposit $1,600 in the account at the end of each year and the account earns 8% interest, compounded annually? (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Round your FV factor to 4 decimal places and final answer to the nearest dollar amount.)

A) $17,280

B) $23,179

C) $27,906

D) $16,000

_____________________________________________

Your grandmother has told you she can either give you $4,700 now or $5,300 when you graduate from college in three years. Your savings account earns 3% interest, compounded annually. Which option would be worth more to you now, and how much more? (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Round your PV factor to 4 decimal places and final answer to 2 decimal places.)

How much will you have in a savings account in ten years, if you deposit $1,600 in the account at the end of each year and the account earns 8% interest, compounded annually? (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1.) (Round your FV factor to 4 decimal places and final answer to the nearest dollar amount.)

A) $17,280

B) $23,179

C) $27,906

D) $16,000

_____________________________________________

Explanation / Answer

Using the formula  FV = p(1+ r) ^n

savings account in ten years

= 1600(1+8/100)^10 + 1600(1+8/100)^9 + 1600(1+8/100)^8 + 1600(1+8/100)^7 + 1600(1+8/100)^6 + 1600(1+8/100)^5 + 1600(1+8/100)^4 + 1600(1+8/100)^3 + + 1600(1+8/100)^2 + + 1600(1+8/100)^1

= 1600 [ (1.08)^10+(1.08)^9 +(1.08)^8 + (1.08)^7 + (1.08)^6 + (1.08)^5 + (1.08)^4 + (1.08)^3 + (1.08)^2 + (1.08)^1 ]

= 1600 [ (1.08)^10 -1 / (1.08 -1) ]

= 1600 [(2.15892499 -1) /0.08 ]

= 20000 (1.15892499 ) = $ 23179 (B) --------------------------------ANSWER

2)

first we find the future value of $4700 after 3 years.

FV = p(1+ r)^n = 4700(1+ 0.03)^3 = 4700(1.03)^3 = $ 5135.8169

Then we find the present value of $5300 in 3 years.

PV = p / (1+ r) ^n = 5300/ (1+ 0.03)^3 = $ 4850.03

So, difference of prsent value of $5300 & $4700 = 4850.03 - 4700 = 150.03

D) The $5,300 in the future is worth $150.03 more than the $4,700 now.

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