Question

Macky Pangan invested ₱2,500 at the end of every 3-month period for 5 years, at 8% interest compounded quarterly. How much is Macky’s investment worth after 5 years?

Answer 1

Compound interest with addition formula:

$A=P(1+\frac{r}{n})^{nt}+\frac{PMT(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}$

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

PMT = Regular contributions (additional money added to investment)

in this example

P = 2500

r = 8% = 0.08

n = 4

t = 5 years

PMT = 2500

$A=2500(1+\frac{0.08}{4})^{4\cdot5}+\frac{2500\cdot(1+\frac{0.08}{4})^{4\cdot5}-1}{\frac{0.08}{4}}$

solving for A:

$A=189408.29$

Therefore, his investment after 5 years will be

$189,408.29