Question

Jonathan deposited $10,500 into a fund at the beginning of every quarter for 17 years. She then stopped making deposits into the fund and allowed the investment to grow for 6 more years. The fund was growing at 6.17% compounded monthly.

a. What was the accumulated value of the fund at the end of year 17?

b. What was the accumulated value of the fund at the end of year 23?

c. What is the total amount of interest earned over the 23-year period?

Answer 1

Effective Rate per quarter:

= ( 1 + r ) ^ n - 1
r = Int Rate per month
n = No.of periods per quarter

Particulars	Amount
Ret period	0.5142%
No. of periods	3.0000

Effective rate per quarter = [ ( 1 + r ) ^ n ] - 1
= [ ( 1 + 0.005142 ) ^ 3 ] - 1
= [ ( 1.005142 ) ^ 3 ] - 1
= [ 1.0155 ] - 1
= 0.0155
I.e Effective rate per quarter is 1.55 %
Part A:

FV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the begining of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity DUe = ( 1 + r ) * FV of Annuity

FV of Annuity = (1+r) * CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$    10,500.00
Int Rate	1.550%
Periods	68

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.0155 ) * [10500 * [ [(1+0.0155)^68] - 1 ] / 0.0155 ]
= ( 1.0155 ) * [10500 * [ [( 1.0155 ) ^ 68 ] - 1 ] / 0.0155 ]
= ( 1.0155 ) * [10500 * [ [ 2.846 ] - 1 ] / 0.0155 ]
= ( 1.0155 ) * [ $ 1250516.98 ]
= $ 1269900.00
Part B:

AMount after 23 Years:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Present Value	$    1,269,900.00
Int Rate	1.5500%
Periods	24

Future Value = Present Value * ( 1 + r )^n
= $ 1269900 ( 1 + 0.0155) ^ 24
= $ 1269900 ( 1.0155 ^ 24)
= $ 1269900 * 1.4465
= $ 1836909.62
Part C:

Int Earned = FV after 23 Years - [ Deposit* No. of deposits ]

= $ 1836909.62 - [ $ 10500 * 68 ]

= $ 1836909.62 - $ 714000

= $ 1122909.62