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

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

$S=R(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})$

$10000=R(\frac{(1+\frac{0.04}{12})^{12*6}-1}{\frac{0.04}{12}})$

$10000=R(\frac{(1+0.00333333333333)^{72}-1}{0.00333333333333})$

$10000=R(\frac{(1.00333333333333)^{72}-1}{0.00333333333333})$

$10000=R(\frac{1.27074187908-1}{0.00333333333333})$

$10000=R(\frac{0.27074187908}{0.00333333333333})$

$10000=R(81.2225637241)$

$\frac{10000}{81.2225637241}=R$

$123.11849739=R$

which is approx $123.

Hence final answer is C) $123.