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Angie borrowed $400 from her parents at 6.5% simple interest for 3 years. What is the total amount Angie must repay?

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2 Answers

simple interest equations:

A = P(1+rt) = P + Prt            

I = Prt                      

A = accumulated amount

P = principal

r = interest rate

t = time (in years)

 

 

angie borrowed $400 (P), so she has to pay it back with interest (I)

I = Prt = $400*0.065*3 = $78

the total paid back is

A = P + I = $400 + $78 = $478

FV = PV(1+r)n

Where

PV = Present Value (in this case PV = $400

FV = Future Value (The value we are solving for)

r = Rate (In this case r = 6.5%. We must convert this to a decimal by diving by 100. r = 0.065)

n = Number of Periods (In ths case n = 3)

FV = $400 (1 + 0.065)3 = $483.18

Another way to think about why this equation works is:

After the first year the amount owed is $400 * 1.065 = $426

After the second year the amount owed is $426 * 1.065 = $453.69

After the third year the amount owed is $453.69 * 1.065 = $483.18

or $400 * 1.065 * 1.065 * 1.065 = $400 (1.065)3 = $483.18