Question

14. Gordon Freeman wants to have $32,000 in 5 years in order to purchase a new car (a) How much should he deposit today in an account earning 6.4%, compounded quarterly, to have the required amount in 5 years? (b) How much interest will be earned? (c) If he can only deposit $16,000 now, how short of $32,000 will he be? (d) Suppose he can deposit $16,000 now in account that compounds interest continuously, What interest rate would he need to accumulate the $32,000 in 5 years?

Answer 1

X for 14a $ 32,000 20 required amount after 5 years quarterly periods quarterly interest rate amount to be deposited today 1.60% $ 23,295.70 interest earned $ 8,704.30 quarterly periods quarterly interest rate amount deposited today amount in account after 5 years he will be short by 20 1.60% $ 16,000 $ 21,978.30 $ 10,021.70 140 amount deposited today required amount after 5 years required interest rate in case of continuous compounding $ 16,000 $32,000 13.86%

for formulas and calculations, refer to the image below -

B2 - x fc 14a required amount after 5 years quarterly periods quarterly interest rate amount to be deposited today 32000 =5*4 =6.4%/4 --PV(D4,D3,0,D2) 14b interest earned =D2-D5 14c quarterly periods quarterly interest rate amount deposited today amount in account after 5 years he will be short by =5*4 =6.4%/4 16000 --FV(D10, D9,0, D11) =32000-D12 14d amount deposited today 16000 required amount after 5 years 32000 required interest rate in case of continuous compounding =LOG(2)/(LOG(EXP(1)}/5

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