$1,202.88
Use the formula for compound interest:
A=P(1+(r/n))^nt
where A is the final amount, P is the initial balance (1,000), r is the interest rate (3.7% is .037), n is the number of times the interest is applied per year (monthly, 12 months in a year is 12) and t is number of years (5)
A=1000(1+(.037/12))^60
A=1202.876 which rounds to 1202.88