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Georgi Rostov deposits $15,000 in a savings account that pays 6% interest compounded monthly
Georgi Rostov deposits $15,000 in a savings account that pays 6% interest compounded monthly. Three years later, he deposits $14,000. Two years later after the $14,000 deposit, he makes another deposit in the amount of $12,500. Four years after the $12,500 deposit, half of the accumulated funds is transferred to a fund that pays 8% interest compounded quarterly. How much money will be in each account six years after the transfer?
Expert Solution
Effective annual interest rate for first account = (1+6%/12)^12 - 1
Effective annual interest rate for first account = 6.1678%
Before 50% withdrawal from first account:
Number of years of deposit for $15000 = 3+2+4 = 9 years
Number of years of deposit for $14000 = 2+4 = 6 years
Number of years of deposit for $12500 = 4 years
So, after 9 years,
Value of funds in first account = 15000*(1+6.1678%)^9 + 14000*(1+6.1678%)^6 + 12500*(1+6.1678%)^4
Value of funds in first account = $61635.3
Now, 50% of this amount is transferred to second account.
So,
Amount to be transferred in second account = 61635.3*.5 = $30817.65
Effective interest rate in second account = (1+8%/4)^4 - 1
Effective interest rate in second account = 8.2432%
So, after 6 years:
Value of amount in first account = 30817.65*(1+6.1678%)^6
Value of amount in first account = $44132.29 or $44132
Value of amount in second account = 30817.65*(1+8.2432%)^6
Value of amount in second account = $49568.21 or $49568
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