Question

Calculate the future value of $500.20, earning interest at a rate of 3 7/8% that is compounded monthly for 4 years.

Answer 1

584.03

Explanation:

Given that principal amount = 500.20 dollars

Interest rate = 3 7/8% p.a.= 3100/8(12) per month

Period = 4 years = 4(12) = 48 months.

A= P(1+r/n)^nt

Here n = 12 t = 4 years.

Substitute to get

Future value =
`500.20(1+(32)/(8(1200)) )^(48)`

=584.03

Answer 2

$583.92

Explanation:

For future value use the formula

`A=P\cdot \left(1+(r)/(n)\right)^(nt),`

where A is future value, P is initial value, n is number of times interest is compounded per year, r is interest rate (as decimal) and t is time (in years).

In your case,

P=$500.20,

r=0.03875 (because 3 7/8%=3.875%),

t=4,

n=12.

Therefore,

`A=500.20\cdot \left(1+(0.03875)/(12)\right)^(12\cdot 4)=500.20(1.00323)^(48)\approx \$583.92.`