Question

Jack wants to buy a boat today today but has realised that if he takes out a loan he can only repay $1200 quarterly, with payments made at the beginning of each quarter, over the next 10 years. How much can he spend on his boat today if the interest rate is 11.6% per annum compounded quarterly?

Select one:

a. $7692.30

b. $28191.63

c. $29009.19

d. $6892.74

Answer 1

We are given,

Quarterly payment(pmt) = $1200

Years = 10

Number of periods(t) = 4 * 10 = 40 ( quarterly payments)

Interest rate(r) = 11.6%/4 = 2.9% (compounded quarterly)

Payments made at the beginning of quarterly

We can calculate Present Value(FV) by the following formula,

PV = pmt1 + pmt2/(1+r)^1 + pmt3/(1+r)^2 +.......pmt40/(1+r)^39

We can also calculate PV using excel,

pmt	1200
no periods	40
interest	2.90%
Present Value	29009.19	(=PV(40,2.90%,-1200,0,1)

Hence the answer is option c) $29009.19

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