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Georgi Rostov deposits $15,000 in a savings account that pays 6% interest compounded monthly

Economics

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?

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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