Question

mother wants to ensure the education of his son. On the 7th birthday of the son, he invest in a fund the amount of P 20000000 earning at 6.5% interest rate compounded monthly; on the 10th birthday another P 20000000 at an interest rate of 7.3% compounded monthly: on the 15th birthday another sum of money at 8% compounded monthly. If on the 18th birthday the son have a total withdrawable amount of P1.3M, how much is the 3rd investment?
correctly answer ASAP Only correct answer will be rated

Answer 1

My assumption on a possible error in the question: In case of first and second investment, the amount invested is P 200,000.00 each and not P 20,000,000 each. I doubt, somebody omitted the dot.


Let maturity amount of first investment of P 200000.00 on 7th birthday = A
Let maturity amount of 2nd investment of P 200000.00 on 10th birthday = B
Let maturity amount of 3rd investment of 'p' amount on 15th birthday = C

We know that on 18th birthday A + B + C = P 1,300,000.00

Now let us compute A first:
Annual rate of interest: 6.5%
Invested amount = P 200000.00
Monthly rate of interest = 6.5%/12 = 0.542%
Tenure = 18th birthday minus 7th birthday =11 years = 132 months

A = 200000*(1+0.00542)¹³²
A = P 408228

Now let us compute B:
Annual rate of interest: 7.3%
Invested amount = P 200000.00
Monthly rate of interest = 7.3%/12 = 0.608%
Tenure = 18th birthday minus 10th birthday = 8 years = 96 months

B = 200000*(1+0.00608)⁹⁶
B = P 357892

Now, we know that A + B + C = P 1,300,000.00
Putting the values of A & B, we get the following:
1300000 = 408228 + 357892 = C
C = 533881

What we do not know here is the investment amount of C investment. Let us assume it to be 'p' and use reverse calcultion on the same formula:

In case of C:
Annual rate of interest: 8%
Monthly rate of interest = 8%/12 = 0.67%
Tenure = 18th birthday minus 15th birthday = 3 years = 36 months

533881 = p x (1+0.0067)³⁶
533881 = p x 1.27
p = 420379

So, the amount invested by mother on her child's 15th birthday was P 420379.