Payments of $6,000.00 are made into a fund at the beginning of each year for ten...

Payments of $6,000.00 are made into a fund at the beginning of each year for ten years. The fund is invested at an annual effective rate of i. The interest generated is reinvested at 10%. The total accumulated value at the end of the ten years is $98,180.00. Find I round to 3 decimal places

Solutions

Expert Solution

Given

Payment each year P=6000

Number of payment N=10

Interest in first account =i

interest in second account r=10%

AV=98180

AV=AV1+AV2

Since interet is reinvested each year in another account so accumultaed amount in first account = Sum of all deposit

AV1=10*6000=60000

98180=60000+AV2

AV2=38180

Future value of interest = Interest *(1+r)^(10-n)

Since interest is reinvested at end of each year so in year ZERo there will be no interest.

Year n	Principle P	Accumulated amount AV	Interest =P*i	FV of interest
0	6000	6000
1	6000	12000	6000i	14147.68i
2	6000	18000	12000i	25723.07i
3	6000	24000	18000i	35076.91i
4	6000	30000	24000i	42517.46i
5	6000	36000	30000i	48315.3i
6	6000	42000	36000i	52707.6i
7	6000	48000	42000i	55902i
8	6000	54000	48000i	58080i
9	6000	60000	54000i	59400i
10			60000i	60000i
		Total AV2 =∑Future value of interest		451870.02i

451870.02i=38180

i=8.449%

jeff jeffy answered 1 year ago

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