Answer to Question #161174 in Financial Math for Hekl

Question

Your grandmother has set up an annuity of $4000 in an account that pays 5.2%/a compounded monthly. What equal monthly payments will the annuity provide for in the next 4 years?

Answer 1

$Fut$$ure value =C {(1+r/k)$^nk -1}/(r/k)

Fv = Future value = $4000

r = interest rate = 5.2%

n = years = 4

k = 12

C = monthly instalment = ?

4000 = C{(1+0.025/12)^4X12 - 1}/(0.052/12)

4000 = C{(1.004333)⁴⁸ - 1}/(0.004333)

4000 = C(1.23064 - 1)/(0.004333)

4000 = C(0.23064/0.004333)

4000 = C(53.2288)

C = 4000/53.2288

C = 75.15

Monthly payments = $75.15