Determine the periodic deposit. Round up to the nearest dolar.

Determine the periodic deposit. Round up to the nearest dolar. How much of the financial goal comes from deposits and how much comes from interest?

Periodic Deposit: $? at the end of every six months

Rate: 6% compounded semiannually

Time: 8 years

Financial Goal: $490,000

Solutions

Expert Solution

The future value (F) of an annuity is given by F = (P/r)[(1+r)ⁿ-1], where P is the periodic payment , r is the rate per period and n is the number of periods.

Here, F = $ 490000, r = 6/200 = 0.03 and n = 8*2 = 16.

Hence 490000 = (P/0.03)[ (1.03)¹⁶ -1] so that P = 490000*0.03/[ (1.03)¹⁶ -1] = 14700/0.604706439 = $ ( on rounding off to the nearest cent).

Thus, the periodic deposit required to achieve the financial goal is $ 24309.32 every six months.

The part of the financial goal that comes from the deposits is 16*$ 24309.32 = $ 388949.12.

The part of the financial goal that comes from the interest is $ 490000-$ 388949.12 = $ 101050.88.

milcah answered 1 year ago

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