1. Simple versus compound interest AaAa Financial contracts involving investment
ID: 2813177 • Letter: 1
Question
1. Simple versus compound interest AaAa Financial contracts involving investments, mortgages, loans, and so on are based on ether a fixed or a variable interest rate. Assume that fixed interest rates are used throughout this question olivia plans to loan $700 to her friend, who will pay a simple interest rate of 8.6% every year for the loan. If no payments are made and no further borrowing occurs between them for nine years, then how much money will Olivia's friend owe her? O $1,470.84 $160.20 O $1,241.80 $765.38 Now, assume that olivia's friend volunteers to pay compound interest instead of simple interest for her loan. If interest is accrued at 8.6% compounded annually, all other things being equal, how much money will Olivia's friend owe her in nine years? O $760.20 $1,470.84 O $1,241.80 O $126.49 Olivia has another investment option in the market that pays 8.6% nominal interest, but it's compounded quarterly Keeping everything else constant, how much money will Olivia have in nine years if she invests $700 in this fund? O $762.17 $1,505.50 O $140.61 O $160.20Explanation / Answer
a.Simple interest=Principal*Interest rate*Time Period
=(700*8.6%*9)=$541.8
Hence total amount owed=Principal+Simple Interest
=(700+541.8)=$1241.80
b.We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.
A=$700*(1.086)^9
=$700*2.101205008
=$1470.84(Approx).
3.
We use the formula:
A=P(1+r/400)^4n
where
A=future value
P=present value
r=rate of interest
n=time period.
Hence
A=$700(1+0.086/4)^(4*9)
=$700*2.150707526
which is equal to
=$1505.50(Approx).
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