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In: Finance

You need to accumulate $10,000. To do so, you plan to make deposits of $1,200 per...

You need to accumulate $10,000. To do so, you plan to make deposits of $1,200 per year - with the first payment being made a year from today - into a bank account that pays 7.6% annual interest. Your last deposit will be less than $1,200 if less is needed to round out to $10,000. How many years will it take you to reach your $10,000 goal? Round your answer up to the nearest whole number.

How large will the last deposit be? Round your answer to the nearest cent.

Solutions

Expert Solution

Total investment to be needed = $ 10,000

Investment of $1200 will be made at the end of each year.

Interest rate received = 7.6%

Interest received in current year will be calculated on basis of Total deposit of previous year.

For example- interest received in year 3 will be = 0.076 *Total deposit of year 2

= 0.076 * 2491.2 = $189.3312 (as on current year deposit of $1200 no interest will be provided as it is made at the end of the year)

Year Deposited
(this year) $		 Interest Received in current year $ Total Deposit (in $)
= total deposit accumulated from last year + deposit this year + interest received
0 0 0 0
1 1200 0 1200
2 1200 91.2 2491.2
3 1200 189.3312 3880.5312
4 1200 294.9203712 5375.451571
5 1200 408.5343194 6983.985891
6 1200 530.7829277 8714.768818
7 622.9087515 662.3224302 10000

Total 7 years it will take you to reach your $10,000 goal.

Last deposit will be of $ 623 (approx)

Hope it helps!

jeff jeffy answered 1 year ago
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