Question

Logan wants to have $130,000 to pay for a surgery on his retractable forearm claws in 30 months. If he can invest money in an account right now that will give him 7.5% interest compounded monthly, how much would he have to
invest now to end up with the amount needed for the surgery later on?

Answer 1

Answer: $107,836.69 or about $107,837 (to the nearest dollar)

Step-by-step explanation:

Formula to the  accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :

$A=P(1+\dfrac{r}{12})^{t}$

As per given , A = $130,000

r= 7.5% = 0.075

t= 30 months

Now,

$130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69$

Hence he need to invest $107,836.69 .