Question

A loan of $2500 has an effective interest rate of 6% annually on the first $1000 of loan balance and 4% effective annually on any excess. Bob wants to repay this loan with level payments at the end of each year over 10 years. Find the level payment.

Answer 1

Assume that Bob has two loans:

The first loan of $1000 with effective interest rate of 6% annually for 10 years

The second loan of $1,500 with effective interest rate of 4% annually for 10 years

Now calculate the level payments for each of the above loans-

We can use PV of an Annuity formula to calculate the annual payment

PV = PMT * [1-(1+i) ^-n)]/i

Where PV (present value of loan) = $1,000

PMT = Annual payment =?

n = N = number of payments = 10

i = I/Y = interest rate per year = 6%

Therefore,         

$1,000 = PMT* [1- (1+6%) ^-10]/6%

PMT = $135.87

Annual payment on first loan is $135.87

Now Annual payment on second loan; we can use PV of an Annuity formula to calculate the annual payment

PV = PMT * [1-(1+i) ^-n)]/i

Where PV (present value of loan) = $1,500

PMT = Annual payment =?

n = N = number of payments = 10

i = I/Y = interest rate per year = 4%

Therefore,                                                                                            

$1,500 = PMT* [1- (1+4%) ^-10]/4%

PMT = $184.94

Annual payment on second loan is $184.94          

The level payments on whole loan for each year = Annual payment on first loan + Annual payment on second loan

= $135.87 + $184.94               

= $320.80

Therefore level payments on the loan are $320.80.