Question

Tony wants to save $10,000 in 6 years. Assuming a 4% interest rate, what is the minimum he must save each month to reach his goal? A) $103 B) $113 C) $123 D) $133

Answer 1

Using the future value of an annuity formula, Tony needs to save approximately $123 each month to achieve his goal of saving $10,000 in 6 years with a 4% interest rate. Thus, the correct answer is: C) $123

Step-by-step explanation:

To calculate the minimum monthly savings needed for Tony to reach his $10,000 goal in 6 years with a 4% interest rate, we use the future value of an annuity formula:

FV = Pmt * (((1 + r)^n - 1) / r), where
FV is the future value,
Pmt is the monthly payment,
r is the monthly interest rate, and
n is the total number of payments.

Given:
FV = $10,000,
r = 4% annual interest rate (which is 0.04 / 12 per month),
n = 6 years * 12 months = 72 payments.

Substituting these values into the formula to solve for Pmt, we get:

Pmt = $10,000 / (((1 + 0.04/12)^72 - 1) / (0.04/12))

After calculating, the monthly payment Tony needs to make is approximately $123. Thus, the correct answer is:

C) $123

Answer 2

We have been given that Tony wants to save $10000 in 6 years.

That means future value S = $10000

Time t= 6 years

Interest rate = 4% yearly = 0.04 yearly

n=12 months per year

Now we have to find monthly payment to recieve $10000 in 6 years. so we need to apply monthly payment formula which is

`S=R(((1+(r)/(n))^(nt)-1)/((r)/(n)))`

`10000=R(((1+(0.04)/(12))^(12*6)-1)/((0.04)/(12)))`

`10000=R(((1+0.00333333333333)^(72)-1)/(0.00333333333333))`

`10000=R(((1.00333333333333)^(72)-1)/(0.00333333333333))`

`10000=R((1.27074187908-1)/(0.00333333333333))`

`10000=R((0.27074187908)/(0.00333333333333))`

`10000=R(81.2225637241)`

`(10000)/(81.2225637241)=R`

`123.11849739=R`

which is approx $123.

Hence final answer is C) $123.