Question

You want to take out a personal loan to finance a trip to Europe. You estimate that you will need $7500 and the bank offers you a 4-year term at 1.98%, compounded quarterly.What will your payments be each month?

Answer 1

Loan amount frm bank = $7500

Interest rate = 1.98% compounded quarterly

Since, the interest rate is compounded quarterly and loan payments are monthly. We will first calculate Nominal Interest rate compounded monthly from compounded quarterly using Annual Effective Interest rate formula:-

where, r1 = Interest rate compounded Quarterly = 1.98%

m1 = n0 of compounding period = 4

r2 = Interest rate compounded Quarterly

m2 = no of compounding period = 12

Taking 12-root on both sides,

r2 = 1.976736%

Now, Calculating the monthly payment of loan:-

Where, P = Loan amount = $7500

r = Periodic Interest rate = 1.976736%/12 = 0.164728%

n= no of periods = 4 years*12 =48

Monthly Paymnet = $162.64

So, your payments be each month is $162.64

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