Suppose that the parents of a young child decide to make annual deposits into a
ID: 1214539 • Letter: S
Question
Suppose that the parents of a young child decide to make annual deposits into a savings account with the first deposit being made on the child's fifth birthday and the last deposit being made on the child's fifteenth birthday. Then, to supplement college expenses, starting on the child's 18th birthday $2,000 will be withdrawn, 19th birthday $2,400, 20th birthday $2,800 and 21st birthday $3,200 will all be made in withdrawals. If the effective annual interest rate is 8% during this period of time, what are the annual deposits in years five through fifteen?
Explanation / Answer
Ans- Here we need to find out annual deposit or fixed deposit int the year 5 through 15.
Suppose the annual deposit per year is =x
In 5th b'day,(x*8/100)=2x/25.
In 6th b'day,(x*8/100)=2x/25.
In 7th b'day,(x*8/100)=2x/25.
In 8th b'day,(x*8/100)=2x/25.
In 9th b'day,(x*8/100)=2x/25.
In 10th b'day,(x*8/100)=2x/25.
In 11th b'day,(x*8/100)=2x/25.
In 12th b'day,(x*8/100)=2x/25.
In 13th b'day,(x*8/100)=2x/25.
In 14th b'day,(x*8/100)=2x/25.
In 15th b'day,(x*8/100)=2x/25.
Total interest rate earned in 11 years are=(2x/25+2x/25+2x/25+2x/25+2x/25+2x/25+2x/25+2x/25+2x/25+2x/25+2x/25)
=11*2x/25=.88x
Maturity value in 11 years will be= (x+.88x)
starting on the child's 18th birthday $2,000 will be withdrawn, 19th birthday $2,400, 20th birthday $2,800 and 21st birthday $3,200 will all be made in withdrawals.
So we can say that, x+.88x=2000+2400+2800+3200
or,1.88x=10400
or,x=10400/1.88=$5531.91
So the annual deposits in years five through fifteen is $5531.91.
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