Question

1. Assuming simple interest determine Paul's initial deposit if his account grew to $4,500 in 7 years, 6 months at an APR of 2.75%

2. Assuming continuous compounding, how much would Susan have to deposit in her account if it grew to $6,000 over 5 years 9 months with an APR of 2.95% ?

Answer 1

1). Final amount = $4500

time period t = 7 years 6 months or 7.5

r = 2.75%

Let principal be P

using simple interest formula, interest is

I = P*r*t = P*0.0275*7.5 = 0.20625P

So, Total amount = P+I = P + 0.20625P = 1.20625P

it is equal to $4500

=> P = 4500/1.20625 = $3730.57

So, initial deposit = $3730.57

2). Given that,

r = 2.95% compounded continuously

Final amount FV = $6000

Time period t = 5 years 9 months or 5.75 years

So, Initial deposit, PV = FV*e^(-r*t)

=> Initial deposit = 6000*e^(-0.0295*5.75) = $5063.59