Question

Kori is making monthly contributions of of $260 to her savings account which pays interest at the APR of 6.9%, compounded monthly. Right after Kori makes her 35th contribution, the bank changes the APR to 7.2% and Kori makes 57 more $260 contributions. What is Kori's balance right after her last contribution?

Answer 1

Annuity is the series of payment made at equal interval , as here Kori is making monthly contribution monthly annuity is given

r=6.9% for annually hence for monthly interest = 0.069/12=0.00575

or 0.575%

FV of Annuity = P[(1+r)n-1]/r

Where P is periodic payment

r is rate of interest

n = number of period or payment

For first 35 contribution

FV = 260[(1+0.069/12)35-1]/(0.069/12)

= 260(1.222226-1)/0.00575

=$10048.48

Now this amount is to compound for 57 more month as it make more 57 payment for which interest rate had been change hence this amound will compound saperately

Compound interest formula

A= P (1+r/n)nt

Where A is Amount

P = Principal ie Amount after 35 month

r = rate of interest

n = number of time interest compounded in a year

nt= 57

=$10048.48(1+0.072/12)57

=$10048.48×1.4063

=$14131.18..........(a)

Now anuuity after rate change for 57 month

=260[(1+0.006)57-1]/0.006

=260[1.4063-1]/0.006

=17606.33

Total Amount after her last contribution = $14131.18+17606.33

=$31737.51