Question

Find the final amount (rounded to the nearest dollar) in the retirement account where $1000 per quarter is invested at 4.2%, compounded quarterly, for 10 years; then while that money is accumulating interest in the new account, a new retirement account is started where $1500 per quarter is invested at 7.4%, compounded quarterly, for 15 years.

Answer 1

The question is solved by calculating the future value of the two accounts.

Account 1

Information provided:

Quarterly investment= $1,000

Time= 10 years*4= 40 quarters

Yield to maturity= 4.2%/4= 1.05% per quarter

Enter the below in a financial calculator to compute the future value:

PMT= 1,000

N= 40

I/Y= 1.05

Press the CPT key and FV to compute the future value.

The value obtained is 49,393.58.

Therefore, the amount in the first account will accumulate to $49,393.58 at the end of 10 years.

Account 2

Information provided:

Quarterly investment= $1,500

Time= 15 years*4= 60 quarters

Yield to maturity= 7.4%/4= 1.85% per quarter

Enter the below in a financial calculator to compute the future value:

PMT= 1,500

N= 60

I/Y= 1.85

Press the CPT key and FV to compute the future value.

The value obtained is 162,465.22.

Therefore, the amount in the second account will accumulate to $162,465.22 at the end of 15 years.

Hence, the final amount in the retirement account is $49,393.58 + $162,465.22 = $211,858.80.