Question

"You deposit $32,000 in a savings account that pays a nominal interest rate of 4.2% compounded monthly. 3 years later, you deposit $14,000. 3 years after the second deposit, you make another deposit in the amount of $9,000. 6 years after the third deposit, half of the accumulated funds are transferred to a fund that pays a nominal interest rate of 6.9% compounded quarterly. How much total will you have in the accounts 4 years after the transfer?"

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Answer 1

First we need to find the effective interest rate per year

The effective annual interest rate is the interest rate that is actually earned or paid on an investment, loan or other financial product due to the result of compounding over a given time period. It is also called the effective interest rate, the effective rate or the annual equivalent rate

So if nominal interest rate (i), number of compounding in a year is (m), effective interest will be

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 4.2% per year

Number of compounding in a year (m) = 12

Let's put all the values in the formula

Effective interest rate = (1 + 0.042/12) ^12 - 1

                                              = (1 + 0.0035) ^12 - 1

                                              = (1.0035) ^12 - 1

                                              = 1.04282 - 1

                                              = 0.0428200000000001

So annual effective interest rate is 4.28% per year

Year	Deposit	FV factor @4.28%	FV of amount
0	32000	1.653530728	52912.98
1
2
3	14,000.00	1.458173504	20414.43
4
5
6	9000	1.285896857	11573.07
7
8
9
10
11
12
		Total	84900.48
		Half amount	42450.24

The second account will earn effective interest of

Effective interest rate = (1 + i/m) ^m -1

Where,

Nominal interest rate (i) = 6.9% per year

Number of compounding in a year (m) = 4

Let's put all the values in the formula

Effective interest rate = (1 + 0.069/4) ^4 - 1

                                              = (1 + 0.01725) ^4 - 1

                                              = (1.01725) ^4 - 1

                                              = 1.07081 - 1

                                              = 0.07081

So annual effective interest rate is 7.08% per year

Accounts	Balance		FV factor	Balance
1	42450.24	FV factor @ 4.28% , 4 years	1.1825	50197.75
2	42450.24	FV factor @ 7.08% , 4 years	1.3147	55810.20

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Hope that helps.

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